Back To Course

High School Geometry: Tutoring Solution14 chapters | 161 lessons

Watch short & fun videos
**Start Your Free Trial Today**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 55,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Maria Airth*

Maria has a Doctorate of Education and over 15 years of experience teaching psychology and math related courses at the university level.

Here, you'll learn the steps to find the perimeter of a square, circle or rectangle from the area of the given shape. You'll also read about the units of measurement used for area, and get tips for solving problems.

Finding the perimeter a shape from its area depends on what shape you are using. To review, **perimeter** is the distance around the edge of a shape, while **area** is the space covered within the edges of a two-dimensional shape.

In this lesson, we'll learn how to find the perimeter of a square, circle or rectangle when given the shape's area.

Let's start with a square and learn by working through this sample problem. Find the perimeter of a square with an area of 64 square meters.

Remember the formulas for both area and perimeter of a square. The area of a square is *a* = *s* 2, or side times side, while the perimeter is *p* = 4*s*, or 4 times *s*.

Find the length of one side by plugging the area value into the formula and solving for s. In this case, 64=*s*2, so *s*=8.

Substitute the value of *s* (the length of a side) into the perimeter formula and solve.

*p* =4 x 8, so *p* = 32

Next, let's look at a sample problem to find the perimeter of a circle form its area. Find the perimeter of a circle with an area of 9pi.

Remember the formulas for both area and perimeter of a circle. The area of a circle is *a* = pi * radius*2, while the perimeter of a circle, more commonly known as the circumference, is *p

Find the length the radius by substituting in the area and solving the formula

9p i= pi * *r*2

Divide by pi to get: 9 = *r*2

*r*=3

Substitute the value of *r* into the perimeter formula

*p* = 2 * pi * 3

*p* = 6pi

It's not possible to determine the perimeter of a rectangle given only the area. The area of a rectangle depends on two unknowns, the length and the width, so you must be given at least one side of the rectangle along with the area to determine the other side and, thus, the perimeter.

Let's look at a sample problem. Find the perimeter of a rectangle with length 4 and area 36m2.

Remember the formula for perimeter and area of a rectangle. The area of a rectangle is *a* = length * width, while the perimeter is *p* = (2 * length) + (2 * width)

Substitute the known values into the area formula

36 = 4 * *w*

36/4 = *w*

*w*=9

Substitute values for length and width into the perimeter formula.

*p* = 2 * 4 + 2 * 9

*p* = 8 + 18 = 26

The answers for each of these calculations will be in **standard units**, not squared. You must use the same measurement that is used in the original problem to format your answer.

In the sample problem for finding perimeter of a square, the area was given in square meters so the perimeter must be given in meters. Thus, the answer is 32m. If the original problem does not give a measurement, no measurement should be used in the answer.

Just as with the square, the answer for the perimeter of a circle should be given in standard units of the original measure unless no measure was given. In this example, no measurement was given so 6 * pi is the answer. The commonly used value of pi is 3.14159, so it is also acceptable to calculate 6 * 3.14159 to get 18.84954 as the answer to the perimeter of this circle.

Similar to the other examples, with a rectangle, if area is given in squared units, the perimeter should be in standard units. Here, the correctly formatted answer is 26m.

Remember that **regular shapes** are shapes with sides that are equal. To find the perimeter of a regular shape from the area of that shape, you need to know the formulas for area and perimeter for the shape.

Step 1 is to plug the area into the area formula and solve for the length of one side. Since it's a regular shape, you know that the sides are all equal.

Step 2 is to plug the side value into the perimeter formula and solve.

Step 3 is simply to ensure correct formatting of the answer. Perimeter is always written in standard units.

To unlock this lesson you must be a Study.com Member.

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
14 in chapter 8 of the course:

Back To Course

High School Geometry: Tutoring Solution14 chapters | 161 lessons

- Parallelograms: Definition, Properties, and Proof Theorems 5:20
- Measuring the Area of a Parallelogram: Formula & Examples 4:02
- What Is a Rhombus? - Definition and Properties 4:24
- Measuring the Area of a Rhombus: Formula & Examples 6:30
- Kites in Geometry: Definition and Properties 4:21
- Rectangles: Definition, Properties & Construction 4:08
- Measuring the Area of a Rectangle: Formula & Examples 4:40
- Squares: Definition and Properties 6:52
- Trapezoids: Definition and Properties 4:24
- Measuring the Area of a Trapezoid 4:38
- Using Heron's Formula in Geometry 5:54
- How to Find the Height of a Parallelogram 3:19
- How to Find the Altitude of a Trapezoid 3:04
- How to Find Perimeter from Area 5:19
- Go to Quadrilaterals: Tutoring Solution

- GACE ESOL Test II: Practice & Study Guide
- GACE Science Test I: Practice & Study Guide
- GACE English Test II: Practice & Study Guide
- GACE ESOL Test I: Practice & Study Guide
- Computer Science 103: Computer Concepts & Applications
- Assessing Student Writing Skills
- Developing Student Vocabularies
- English Language Learners Instruction
- Understanding Computer Files
- Strategies for Developing Student Writing Skills
- Common Core State Standards in Ohio
- Resources for Assessing Export Risks
- Preview Personal Finance
- California School Emergency Planning & Safety Resources
- Popsicle Stick Bridge Lesson Plan
- California Code of Regulations for Schools
- WV Next Generation Standards for Math

- Chinese Cinderella: Characters & Quotes
- Local, National & Global Business: Definitions & Examples
- Cell Membrane Analogies
- Implications of Choice Theory on Social Policy & Crime
- The Greensboro Sit-In: Summary & Significance
- Scaffolding Strategies that Support Academic Language Proficiency
- Tarsier Monkey: Life Cycle & Reproduction
- Pig Farming Facts: Lesson for Kids
- Chemical Properties: Quiz & Worksheet for Kids
- Quiz & Worksheet - Endoplasmic Reticulum Facts for Kids
- Quiz & Worksheet - Indecent Exposure as a Legal Issue
- Boston Massacre Significance: Quiz & Worksheet for Kids
- Quiz & Worksheet - Nucleolus Facts for Kids
- Growth & Opportunity for Entrepreneurs Flashcards
- Understanding Customers as a New Business Flashcards

- History 108: History of the Vietnam War
- 7th Grade Earth Science: Enrichment Program
- Introduction to Environmental Science: Help and Review
- Praxis Spanish Exam: Practice & Study Guide
- Introduction to Astronomy: Certificate Program
- Saxon Algebra 1/2: Graphs on the Coordinate Plane
- MTEL Speech: Using Communication Aids for Speeches
- Quiz & Worksheet - The Adenoviridae Virus Family
- Quiz & Worksheet - USSR History
- Quiz & Worksheet - Society & Culture in the 1700s
- Quiz & Worksheet - Life & Works of Benjamin Franklin
- Quiz & Worksheet - Writing Strong Paragraphs in Business Communications

- Demand-Pull Inflation vs Cost-Push Inflation
- Lewis Henry Morgan: Theory & Biography
- Buoyancy Experiments for Kids
- Fieldtrip Checklist for Teachers
- Cell Analogy Project Ideas
- Does Your High School GPA Matter?
- Finding Continuing Education Grants for Teachers
- How to Pass the CPC Exam
- Love Quotes in Translated Literature
- What is Micro Credentialing?
- How to Multitask
- Math Riddles for Adults

Browse by subject