Introduction
Perimeter of Polygons is an important Grade 3 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with perimeter of polygons.
What Is Perimeter of Polygons?
Perimeter of Polygons means finding the distance around a polygon by adding the side lengths carefully.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Perimeter of Polygons
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: What is the perimeter of this rectangle in units?
- A. \(9\) units
- B. \(18\) units
- C. \(36\) units
- D. \(54\) units
Why it works: \(P = 2(6) + 2(3) = 12 + 6 = 18\) units.
Answer: \(18\) units
Visual Model 2
Question: This is a square with side length \(4\) m. What is its perimeter?
- A. \(8\) m
- B. \(12\) m
- C. \(16\) m
- D. \(24\) m
Why it works: A square has 4 equal sides. \(P = 4 + 4 + 4 + 4 = 16\) m.
Answer: \(16\) m
Worked Examples
Example 1
Question: What is the perimeter of this rectangle in centimeters?
- A. \(7\) cm
- B. \(14\) cm
- C. \(10\) cm
- D. \(28\) cm
- \(P = 2(5) + 2(2) = 10 + 4 = 14\) cm.
Answer: \(14\) cm
Example 2
Question: What is the perimeter?
- A. \(9\) units
- B. \(18\) units
- C. \(28\) units
- D. \(35\) units
- \(P = 2(7) + 2(2) = 14 + 4 = 18\) units.
Answer: \(18\) units
Example 3
Question: This is a square with side \(3\) inches. Find its perimeter.
- A. \(9\) in
- B. \(15\) in
- C. \(12\) in
- D. \(18\) in
- \(P = 4 \times 3 = 12\) in.
Answer: \(12\) in
Real-World Word Problems
Problem 1
Question: A rectangle has length \(10\) inches and width \(4\) inches. Find the perimeter.
- A. \(28\) in
- B. \(14\) in
- C. \(40\) in
- D. \(56\) in
Why it works: \(P = 2(10) + 2(4) = 20 + 8 = 28\) in.
Answer: \(28\) in
Problem 2
Question: A square has a perimeter of \(20\) feet. What is the length of one side?
- A. \(5\) ft
- B. \(4\) ft
- C. \(10\) ft
- D. \(20\) ft
Why it works: A square has 4 equal sides. \(20 \div 4 = 5\) ft per side.
Answer: \(5\) ft
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
A rectangle has length \(8\) cm and width \(5\) cm. What is its perimeter?
- A. \(13\) cm
- B. \(26\) cm
- C. \(40\) cm
- D. \(80\) cm
Question 2
A rectangle's length is \(12\) cm. Its width is \(3\) cm. What is the perimeter?
- A. \(15\) cm
- B. \(36\) cm
- C. \(30\) cm
- D. \(72\) cm
Question 3
Which of these has a perimeter of \(24\) feet?
- A. Square with side \(4\) ft
- B. Rectangle with length \(6\) ft and width \(3\) ft
- C. Square with side \(5\) ft
- D. Rectangle with length \(8\) ft and width \(4\) ft
Question 4
A rectangle has perimeter \(20\) cm. If the length is \(6\) cm, what is the width?
- A. \(4\) cm
- B. \(2\) cm
- C. \(8\) cm
- D. \(14\) cm
Question 5
Find the perimeter.
- A. \(10\) m
- B. \(16\) m
- C. \(20\) m
- D. \(24\) m
Question 6
A rectangle has length \(7\) units and width \(3\) units. What is its perimeter?
- A. \(10\) units
- B. \(21\) units
- C. \(28\) units
- D. \(20\) units
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(26\) cm
Perimeter \(=2\ell+2w=2(8)+2(5)=16+10=26\) cm.
Question 2
Answer: \(30\) cm
\(P = 2(12) + 2(3) = 24 + 6 = 30\) cm.
Question 3
Answer: \(P = 2(8) + 2(4) = 16 + 8 = 24\) ft
Option D is correct: \(2(8) + 2(4) = 24\) ft. Option A is \(16\) ft, option B is \(18\) ft, and option C is \(20\) ft.
Question 4
Answer: \(4\) cm
\(P = 2\ell + 2w\), so \(20 = 2(6) + 2w = 12 + 2w\). Thus \(2w = 8\) and \(w = 4\) cm.
Question 5
Answer: \(20\) m
\(P = 2(8) + 2(2) = 16 + 4 = 20\) m.
Question 6
Answer: \(20\) units
\(P = 2(7) + 2(3) = 14 + 6 = 20\) units.
Connection to Standards
This lesson supports Grade 3 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Perimeter of Polygons becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
