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Geometry Math Problems - Perimeters

In these lessons, we will learn to solve geometry math problems that involve perimeter.

Related Pages Geometry math problems involving area Area Formula Geometry math problems involving angles More Algebra Word Problems

Geometry word problems involves geometric figures and angles described in words. You would need to be familiar with the formulas in geometry.

Making a sketch of the geometric figure is often helpful.

Geometry Word Problems Involving Perimeter

Example: A triangle has a perimeter of 50. If 2 of its sides are equal and the third side is 5 more than the equal sides, what is the length of the third side?

Solution: Step 1: Assign variables:

Let x = length of the equal sides Sketch the figure

Step 2: Write out the formula for perimeter of triangle .

P = sum of the three sides

Step 3: Plug in the values from the question and from the sketch.

50 = x + x + x+ 5

Combine like terms 50 = 3x + 5

Isolate variable x 3x = 50 – 5 3x = 45 x = 15

Be careful! The question requires the length of the third side.

The length of third side = 15 + 5 = 20

Answer: The length of third side is 20.

Geometry Math Problem involving the perimeter of a rectangle

The following two videos give the perimeter of a rectangle, a relationship between the length and width of the rectangle, and use that information to find the exact value of the length and width.

Example: A rectangular garden is 2.5 times as long as it is wide. It has a perimeter of 168 ft. How long and wide is the garden?

Example: A rectangular landing strip for an airplane has perimeter 8000 ft. If the length is 10 ft longer than 35 times the width, what is the length and width?

Examples of perimeter geometry word problems This video shows how to write an equation and find the dimensions of a rectangle knowing the perimeter and some information about the about the length and width.

Example: The width of a rectangle is 3 ft less than its length. The perimeter of the rectangle is 110 ft. Find the dimensions.

Perimeter Word Problems

Example: The length of a rectangle is 7 cm more than 4 times its width. Its perimeter is 124 cm. Find its dimensions.

Geometry Math Problem involving the perimeter of a triangle

The following two videos give the perimeter of a triangle, a relationship between the sides of the triangle, and use that information to find the exact value or values of the required side or sides.

Example: Patrick’s bike ride follows a triangular path; two legs are equal, the third is 8 miles longer than the other legs. If Patrick rides 30 miles total, what is the length of the longest leg?

Example: The perimeter of a triangle is 56 cm. The first side is 6 cm shorter than the second side. The third side is 2 cm shorter than twice the length of the first side. What is the length of each side?

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Free geometry tutorials on topics such as perpendicular bisector, central and inscribed angles, circumcircles, sine law and triangle properties to solve triangle problems. Also geometry problems with detailed solutions on triangles, polygons, parallelograms, trapezoids, pyramids and cones are included. Polar coordinates equations, conversion and graphing are also included. More challenging geometry problems are also included.

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• How to construct a frustum? . If you cut off the top part of a cone with a plane perpendicular to the height of the cone, you obtain a conical frustum. How to construct a frustum given the radius of the base, the radius of the top and the height?
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Geometry Tutorials

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• Triangles . Definitions and properties of triangles in geometry.
• Area of Triangles Problems with Solutions . Use different formulas of the area of a triangle to calculate the areas of triangles and shapes.
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• Triangles, Bisectors and Circumcircles - interactive applet . The properties of perpendicular bisectors in triangles and circumcircles are explored interactively using a geometry Java applet.
• Quadrilaterals , properties and formulas.
• Kite Questions with Solutions .
• Angles in Geometry . Definitions and properties of angles in geometry including questions with solutions.
• Angles in Parallel Lines and Transversals . This tutorial is about the corresponding, interior and exterior angles formed when a transversal line intersects two parallel lines.
• Latitude and Longitude Coordinate System .
• Find the GPS Latitude and Longitude Using Google Map .
• Regular Polygons . Tutorial to develop useful formulas for area of regular polygons.

Other Geometry Topics

• Perpendicular Bisector Problems with Solutions .
• Table of Formulas for Geometry . A table of formulas for geometry, related to area and perimeter of triangles, rectangles, circles, sectors, and volume of sphere, cone, cylinder are presented.

Challenge Geometry Problems

• Two Tangent Circles and a Square - Problem With Solution . You are given the perimeter of a small circle to find the radius of a larger circle inscribed within a square.
• Kite Within a Square - Problem With Solution . A problem on finding the sine of the angle of a kite within a square.
• Solve Triangle Given Its Perimeter, Altitute and Angle - Problem With Solution .
• Solve Right Triangle Given Perimeter and Altitude - Problem With Solution .
• Triangle and Tangent Circle - Problem With Solution . A problem, on a triangle tangent at two points to a circle, is presented along with detailed solution.
• Three Tangent Circles - Problem With Solution . A problem, on three tangent circles, is presented along with solution.
• Equilateral Triangle Within a Square - Problem With Solution . A problem on the proof of an equilateral triangle within a square is presented along with detailed solution.
• Square Inscribed in Right Triangle - Problem With Solution . Find the side of a square inscribed in a right triangle given the sides of the triangle.

Polar Coordinates

• Plot Points in Polar Coordinates . An interactive tutorial on how to plot points given by their polar coordinates.
• Graphing Polar Equations . This is tutorial on graphing polar equations by hand, or sketching, to help you gain deep understanding of these equations. Several examples with detailed solutions are presented.
• Convert Polar to Rectangular Coordinates and Vice Versa . Problems, with detailed solutions, where polar coordinates are converted into rectangular coordinates and vice versa are presented.
• Convert Equation from Rectangular to Polar Form . Problems were equations in rectangular form are converted to polar form, using the relationship between polar and rectangular coordinates, are presented along with detailed solutions.
• Convert Equation from Polar to Rectangular Form . Equations in polar form are converted into rectangular form, using the relationship between polar and rectangular coordinates. Problems with detailed solutions are presented.

Geometric Transformations

• Reflection Across a Line . The properties of reflection of shapes across a line are explored using a geometry applet.
• Rotation of Geometric Shapes . The rotations of 2-D shapes are explored.

Geometric Calculators and Worksheets

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Fourth Grade Math With Confidence

Everything you need to know about Fourth Grade Math with Confidence. Includes an overview of what your child will learn, a downloadable sample, answers to frequently asked questions, and buying information.

In this article, you’ll find all the information specific to Fourth Grade Math with Confidence :

• How the program and lessons are organized
• What your child will learn
• What you’ll need
• Placement advice
• Where to buy the books

For information about the series as a whole (or information on other grade levels ), please see this article: Overview of Math with Confidence Homeschool Math Curriculum .

Wishing you all the best in your teaching! Happy Fourth Grade Math!

What’s the program’s format?

Fourth Grade Math with Confidence is a complete fourth-grade math program with three volumes : an Instructor Guide and two Student Workbooks. 

• The  Instructor Guide  is the core of the program, with conversational and hands-on activities and games that teach the key skills and concepts.
• The  two Student Workbooks (Part A and Part B ) provide lesson activities, practice, and review. Workbook Part A covers Units 1-8, and Workbook Part B covers Units 9-16.

Fourth Grade Math with Confidence has 16 units in all. Units vary in length from 6 to 12 lessons, and there are a total of 144 lessons. 128 are regular lessons, and 16 are optional enrichment lessons.

You’re welcome to adjust the number of lessons you teach per week to best fit your family’s schedule. Some families prefer to teach math 5 days per week, while others prefer to teach math 4 days per week and leave one day open for co-ops, errands, or field trips. If you teach 4 lessons per week and teach all the enrichment lessons, the program will take you 36 weeks. If you teach 4 lessons per week and skip the enrichment lessons, the program will take you 32 weeks.

If you used Third Grade Math with Confidence, you’ll find the format for Fourth Grade very familiar. It has the same overall flow to the lessons, with three workbook pages per lesson and a unit wrap-up at the end of each unit.

What does a typical lesson look like?

Most pilot families spent an average of 25-35 minutes on each lesson, with 10-15 minutes of parent-led instruction and 15-20 minutes of independent work. However, this will vary depending on your teaching style and your child’s learning style—and whether you have any toddlers interrupting you!

Each lesson includes 3 parts:

• Memory Work and Warm-up. Each lesson begins with a few memory work review questions and a quick warm-up activity. The warm-up activity eases your child into math time and helps start the lesson on a confident and positive note.
• Lesson Activities with Parent . Next, you’ll use the scripted lesson plan and Lesson Activities page in the workbook to teach your child new concepts and skills. For example, you might roll dice to play an angle identification game, use pattern blocks to add mixed numbers, or use a timer (or timer app) to explore hundredths of a second.
• Independent Practice . Last, your child will complete the Practice and Review workbook pages. On the Practice page, he’ll practice the new concept or skill you taught him. On the Review page, he’ll review previously-learned skills so that he retains them well.

For example, in lesson 5.5, you’ll use the scripted lesson in the Instructor Guide and this Lesson Activities page to introduce mental division. You’ll use play money to model the problems, and then your child will spin the wheel at the the “mental math arcade” to apply his new skills in a real-life context.

Then, your child will then independently practice mental division on the Practice page and review skills like multiplying fractions, place value, multi-digit addition and subtraction, and the distributive property on the Review page.

Can I download a sample?

Yes indeed! You’ll find the full introduction, scope and sequence, and materials list, plus a variety of lessons  from across the year so that you get a good sense of the program as a whole. Make sure to download both files so that you can see how the Instructor Guide complements the Student Workbook.  

• Download : Instructor Guide sample
• Download : Student Workbook sample

What will my child learn?

Fourth Grade Math with Confidence is a full-year, comprehensive curriculum that covers everything your child needs to learn in fourth grade. She’ll learn how to:

• Understand place value in numbers to the millions-place
• Identify factors or multiples of numbers and tell whether numbers are prime or composite
• Solve multiplication problems (up to four-digit times one-digit and two-digit times two-digit)
• Use long division to solve division problems (up to four-digit divided by one-digit)
• Convert improper fractions to mixed numbers and vice versa
• Add and subtract fractions and mixed numbers with like denominators
• Multiply fractions by whole numbers
• Multiply to create equivalent fractions
• Read, write, compare, and order decimals to the hundredths place
• Solve measurement problems and convert measurements within a system of measurement (for example, inches to feet, or kilograms to grams)
• Measure, draw, compare, and reason about angles
• Identify and categorize triangles and quadrilaterals
• Create and interpret line plots
• Find averages

What materials will I need?

I’ve kept the materials list as simple and budget-friendly as possible, just like in the earlier levels of Math with Confidence: counters, play money, pattern blocks , base-ten blocks , a ruler, a protractor, 2 packs of playing cards, 2 dice, blank paper, and pencils. (Note that you’ll use base-ten blocks only occasionally. If you don’t already own them, you may want to copy and cut out the paper blocks in the back of the book rather than buying them.)

Is my child ready to start Fourth Grade Math with Confidence ?

Your child is ready to start Fourth Grade Math with Confidence if she can:

• Read, write, compare, and understand place value in numbers to 10,000
• Use the traditional process to add and subtract 4-digit numbers written vertically. (You might know these problems as “stack math” or “borrowing and carrying.”)
• Name answers to the multiplication and division facts (up to 10×10 and 100÷10). She should be able to recall the answers to most within 3 seconds or so. It’s okay if she’s still developing fluency with the tricky 7s, 8s, and 9s.
• Use addition, subtraction, multiplication, and division to solve word problems, including two-step word problems.
• Find the area and perimeter of rectangles.
• Read, write, and compare simple fractions.

(Note that this is the bare minimum list of skills your child should know before starting Fourth Grade Math with Confidence. It is not a full list of everything covered in Third Grade Math with Confidence.)

If your child is not fluent with the multiplication and division facts but knows the rest of the skills listed above, he is probably ready to begin Fourth Grade Math with Confidence. Make sure to add 5 minutes of daily multiplication fact or division fact practice to each lesson until your child becomes more fluent with the facts.

If you have more questions about placement, check out this article for more advice and answers to frequently asked questions:

• Related : How to Choose the Right Level of Math with Confidence for Your Child

How are enrichment activities and picture books incorporated?

Each unit also includes an enrichment lesson with a picture book and real-life math application activity. These are completely optional , and you can include as many or as few as you want over the course of the year. Many of them are also available as read-alouds on Youtube.

• Related : Fourth Grade Math with Confidence Picture Book List

Will there be other grades? Is Math with Confidence a full series?

Yes! Math with Confidence will be a comprehensive kindergarten through sixth grade math curriculum once it’s complete. See this article for the release dates and more information on other grades.

Where can I buy Fourth Grade Math with Confidence ?

Publication day is June 11, 2024. Print copies will be available at Well-Trained Mind Press , Amazon , and homeschool booksellers.

Digital copies (PDFs) will only be available directly from Well-Trained Mind Press .  

1 thought on “Fourth Grade Math With Confidence”

Can you tell me how MWC compares to Right Start? My daughter is finishing level D and has a rough time with her attitude towards math. We tried Singapore a short bit and went back to right start. I’m trying to figure out if it would be a difficult transition from RS to MWC. I’m thinking the student workbook would really help my rising 4th grader out but I don’t want to rock the boat by switch curriculum again.

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An inverse source problem for a pseudoparabolic equation with memory

• M. J. Huntul 1 ,  ,  , 
• Kh. Khompysh 2 , 
• M. K. Shazyndayeva 2 , 
• M. K. Iqbal 3
• 1. Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia
• 2. Al-Farabi Kazakh National University, Almaty, Kazakhstan
• 3. Department of Mathematics, Government College University, Faisalabad, Pakistan
• Received: 28 January 2024 Revised: 10 April 2024 Accepted: 11 April 2024 Published: 18 April 2024

MSC : 35R30, 35K10, 35A09, 35A01, 35A02

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This paper is devoted to investigating the well-posedness, as well as performing the numerical analysis, of an inverse source problem for linear pseudoparabolic equations with a memory term. The investigated inverse problem involves determining a right-hand side that depends on the spatial variable under the given observation at a final time along with the solution function. Under suitable assumptions on the problem data, the existence, uniqueness and stability of a strong generalized solution of the studied inverse problem are obtained. In addition, the pseudoparabolic problem is discretized using extended cubic B-spline functions and recast as a nonlinear least-squares minimization of the Tikhonov regularization function. Numerically, this problem is effectively solved using the MATLAB subroutine lsqnonlin . Both exact and noisy data are inverted. Numerical results for a benchmark test example are presented and discussed. Moreover, the von Neumann stability analysis is also discussed.

• inverse problem ,
• pseudoparabolic equation ,
• memory term ,
• Tikhonov regularization ,
• stability analysis ,
• nonlinear optimization

Citation: M. J. Huntul, Kh. Khompysh, M. K. Shazyndayeva, M. K. Iqbal. An inverse source problem for a pseudoparabolic equation with memory[J]. AIMS Mathematics, 2024, 9(6): 14186-14212. doi: 10.3934/math.2024689

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• This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/4.0/ -->

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• © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/4.0 )

通讯作者: 陈斌, [email protected]

沈阳化工大学材料科学与工程学院 沈阳 110142

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• Figure 1. The analytical solution given by (6.5), the approximate curves and the absolute computational error for the direct problem given by (2.5)–(2.7) by using $ \Delta x = \Delta t = \frac{1}{20}, \frac{1}{40}, \frac{1}{80} $
• Figure 2. (a) The $ J $ from (5.2) and (b) the exact (6.4) and approximate solutions for $ f(x) $, with $ p = 0 $ and $ \delta = 0 $, for (2.5)–(2.8)
• Figure 3. The exact (6.4) and approximate solutions for $ f(x) $, for $ p = 0.01\% $ with (a) $ \delta = 0 $ and (b) $ \delta\in \{10^{-9}, 10^{-8}\} $ for (2.5)–(2.8)
• Figure 4. The exact (6.4) and approximate solutions for $ f(x) $, for $ p = 0.1\% $ with (a) $ \delta = 0 $ and (b) $ \delta\in \{10^{-8}, 10^{-7}\} $ for (2.5)–(2.8)
• Figure 5. The absolute error between the analytical (6.5) and approximate solutions for $ u(x, t) $, with (a) $ \delta = 0 $, (b) $ \delta = 10^{-8} $ and (c) $ \delta = 10^{-7} $ for $ p = 0.1\% $ noise, for (2.5)–(2.8)

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How UConn masterfully baited Purdue and Zach Edey into a math problem en route to its second national title

Uconn flexed its defensive smarts with a dominant game plan to cork one of purdue's best weapons.

GLENDALE, Ariz. -- Purdue star Zach Edey won the battle of the big men in Monday night's national championship game, but UConn center Donovan Clingan and his Huskies ultimately won the war. The 2023 champs strategically picked apart the Boilermakers with a defensive game plan so sound it made Purdue abandon one of its most potent weapons, the 3-point shot, and in the process scored a 75-60 win inside State Farm Stadium to become the first repeat title winners since Florida in 2007.

UConn could have helped Clingan handle the Naismith Player of the Year in the post. Instead, it allowed Clingan and Samson Johnson to go head-to-head with the 7-4 giant. Purdue, which entered the game second in the country in shooting 40.6% from 3, finished 1-for-7 from beyond the arc on the day. UConn cut off the shot menu almost entirely by daring Edey and his team to feast on a heavy diet of mid-range jumpers and Edey hook shots in one-on-one situations.

Purdue's seven 3-point attempts was the fewest by a team in the title game since UConn in 1999 and the fewest by any team in this year's tournament. Its one made 3-point shot tied for the fewest in a national title game. 

"We didn't want to give up 3s," Huskies coach Dan Hurley said. "We didn't care if Zach took 25, 28 shots to get 30, 35 points. This whole game plan was, like, no (Braden) Smith, no (Fletcher) Loyer, no (Mason) Gillis, no (Lance) Jones. Keep that collective group under 18, 20 points. They had no chance to win, no matter how well Zach played."

It came down to a math problem for Purdue. It could shoot 40+ percent from the field -- which it did -- and still lose by 15 -- again, which it did! -- if UConn effectively wiped the 3-point shot from Purdue's arsenal. Edey had 37 points and finished 15-of-25 shooting. But one made 3 from Purdue as a team put the Boilermakers in a position to try and play a losing numbers game. It engaged in that game and lost.

Take the first points of the game from Edey as an example. On its face, two points on a hook shot from Edey is Purdue's bread and butter -- and this is seemingly a win for the two-time player of the year. But check the strategy here: UConn doesn't send help down to the post and lets Edey shoot inside the paint, opting instead to focus on remaining attached to the shooters surrounding the perimeter.

Tristen Newton , who was named the Final Four's Most Outstanding Player after scoring 20 points and added seven assists and five rebounds, said he felt the defensive game plan worked to perfection. The goal was to limit 3-point attempts and to stay home on all shooters. That meant Clingan had to carry a big lift as the primary defender for Edey in one-on-one situations in the paint, but defending on an island also meant that good 3-point shooters for Purdue wouldn't be turned loose with high frequency.

"[Purdue] gets its 3-pointers off when people go down there and help on Edey," Newton said. "They did a great job planning and made sure it was a focus that we didn't leave the three-point line and let Edey do his damage. He only shoots 2s. He doesn't shoot 3s. If he makes 15 2s like he did today, that's 30. Where are the rest of the points going to come from?"

Good question. The answer: Braden Smith had 12 points on 4-of-12 shooting, Lance Jones had five points on 2-of-3 shooting, Trey Kaufman-Renn had four points on four shots and Cam Heide had two spectacular points off an incredible putback. That was it. And the only 3-pointer Purdue made came late in the shot clock from Smith off what Hurley called a "late clock mistake."

That meant that Purdue had to take what it was given. And in this case, the Boilermakers' best player taking 25 shots may have ultimately been to their own demise.

"We were one-dimensional because of how good Zach Edey is," Purdue coach Matt Painter said. "We were comfortable going to him, right? We were comfortable continuing to do that. That's what they're giving you."

"They're a great defensive team," he added. "So they just made a decision, like, we can defend the perimeter and we can take this away from you, then you're just going to get the ball to your best player, he's going to be one on one, then that's that."

Painter seemed content with his team's ability to remain poised despite being forced to be one-dimensional on offense. But feeding Edey in the paint and settling for shots inside the arc ultimately played right into UConn's hands. More shots inside the arc for Purdue meant more bodies and more length to contest for UConn and it reduced the chance of the Boilermakers heating up from deep to go on any type of run. Once UConn gained control it retained control and slowly squeezed the life out of its opponent. 

On a night dominated by UConn and in a season dominated by its offense, which finished No. 1 in adjusted efficiency ratings at KenPom, it's only fitting that the best team won with a superior effort from its defense to clinch this year's tournament title in the same fashion it has won all season long.

"Obviously, what could you say?" Hurley said. "We won by a lot -- again."

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Unit 7: Area and perimeter

About this unit.

Area and perimeter help us measure the size of 2D shapes. We’ll start with the area and perimeter of rectangles. From there, we’ll tackle trickier shapes, such as triangles and circles.

Count unit squares to find area

• Intro to area and unit squares (Opens a modal)
• Measuring rectangles with different unit squares (Opens a modal)
• Measuring area with partial unit squares (Opens a modal)
• Creating rectangles with a given area 1 (Opens a modal)
• Creating rectangles with a given area 2 (Opens a modal)
• Find area by counting unit squares 7 questions Practice
• Find area with partial unit squares 7 questions Practice
• Create rectangles with a given area 4 questions Practice

Area of rectangles

• Transitioning from unit squares to area formula (Opens a modal)
• Finding missing side when given area (Opens a modal)
• Counting unit squares to find area formula (Opens a modal)
• Area of rectangles review (Opens a modal)
• Transition from unit squares to area formula 7 questions Practice
• Find a missing side length when given area 7 questions Practice
• Perimeter: introduction (Opens a modal)
• Perimeter of a shape (Opens a modal)
• Find perimeter by counting unit squares (Opens a modal)
• Finding perimeter when a side length is missing (Opens a modal)
• Finding missing side length when given perimeter (Opens a modal)
• Perimeter & area (Opens a modal)
• Perimeter and unit conversion (Opens a modal)
• Applying the metric system to perimeter (Opens a modal)
• Perimeter review (Opens a modal)
• Find perimeter by counting units 4 questions Practice
• Find perimeter when given side lengths 7 questions Practice
• Find a missing side length when given perimeter 4 questions Practice

Area of parallelograms

• Area of a parallelogram (Opens a modal)
• Area of parallelograms (Opens a modal)
• Area of parallelograms 4 questions Practice
• Find missing length when given area of a parallelogram 4 questions Practice

Area of triangles

• Area of a triangle (Opens a modal)
• Area of triangles (Opens a modal)
• Area of triangle proof (Opens a modal)
• Find base and height on a triangle 4 questions Practice
• Area of right triangles 4 questions Practice
• Area of triangles 7 questions Practice
• Find missing length when given area of a triangle 4 questions Practice

Area of shapes on grids

• Area of a triangle on a grid (Opens a modal)
• Area of a quadrilateral on a grid (Opens a modal)
• Areas of shapes on grids 4 questions Practice

Area of trapezoids & composite figures

• Area of trapezoids (Opens a modal)
• Area of kites (Opens a modal)
• Finding area by rearranging parts (Opens a modal)
• Area of composite shapes (Opens a modal)
• Perimeter & area of composite shapes (Opens a modal)
• Challenge problems: perimeter & area (Opens a modal)
• Area of trapezoids 4 questions Practice
• Area of composite shapes 4 questions Practice
• Area challenge 4 questions Practice

Area and circumference of circles

• Radius, diameter, circumference & π (Opens a modal)
• Labeling parts of a circle (Opens a modal)
• Radius, diameter, & circumference (Opens a modal)
• Circumference review (Opens a modal)
• Radius & diameter from circumference (Opens a modal)
• Area of a circle (Opens a modal)
• Area of circles review (Opens a modal)
• Area of a circle intuition (Opens a modal)
• Radius and diameter 7 questions Practice
• Circumference of a circle 4 questions Practice
• Area of a circle 7 questions Practice
• Area of parts of circles 4 questions Practice

Advanced area with triangles

• Area of equilateral triangle (Opens a modal)
• Area of equilateral triangle (advanced) (Opens a modal)
• Area of diagonal-generated triangles (Opens a modal)