Perimeter and Area

Grade 7 Math - Perimeter and Area

Lesson Objectives

Define perimeter and area of 2D shapes.
Calculate perimeter of regular and irregular shapes.
Understand the concept of area and apply formulas for basic shapes.

Lesson Introduction

Whether it's fencing a garden or laying tiles on the floor, perimeter and area play a crucial role in everyday life. In this lesson, we will explore how to calculate the distance around shapes (perimeter) and how to find the amount of space they cover (area).

Core Lesson Content

Perimeter: The perimeter of a shape is the total distance around its edges.

For rectangles: $P = 2(l + w)$
For squares: $P = 4s$
For triangles: $P = a + b + c$

Area: The area of a shape is the amount of surface it covers.

Rectangle: $A = l \times w$
Square: $A = s \times s = s^2$
Triangle: $A = \frac{1}{2} \times b \times h$

Worked Examples

Example 1: Find the perimeter of a square with side 6 cm.

P = 4s = 4 \times 6 = 24 \text{ cm}

Explanation: A square has 4 equal sides.

Example 2: Calculate the perimeter of a rectangle with length 10 cm and width 5 cm.

P = 2(l + w) = 2(10 + 5) = 2 \times 15 = 30 \text{ cm}

Explanation: Add length and width, then multiply by 2.

Example 3: What is the perimeter of a triangle with sides 5 cm, 7 cm, and 8 cm?

P = 5 + 7 + 8 = 20 \text{ cm}

Explanation: Sum the lengths of all three sides.

Example 4: Find the area of a rectangle with length 12 m and width 4 m.

A = l \times w = 12 \times 4 = 48 \text{ m}^2

Explanation: Multiply length by width.

Example 5: Find the area of a square with side 9 cm.

A = s^2 = 9 \times 9 = 81 \text{ cm}^2

Explanation: Multiply the side by itself.

Example 6: A triangle has base 10 cm and height 6 cm. Find its area.

A = \frac{1}{2} \times b \times h = \frac{1}{2} \times 10 \times 6 = 30 \text{ cm}^2

Explanation: Use the triangle area formula.

Example 7: A rectangular field is 25 m long and 15 m wide. What is its perimeter and area?

P = 2(25 + 15) = 2 \times 40 = 80 \text{ m}

A = 25 \times 15 = 375 \text{ m}^2

Explanation: Apply both formulas.

Example 8: A square garden has a perimeter of 36 m. Find the length of one side.

P = 4s \Rightarrow 36 = 4s \Rightarrow s = \frac{36}{4} = 9 \text{ m}

Explanation: Divide perimeter by 4.

Example 9: A triangle has two equal sides of 7 cm and a base of 6 cm. Find the perimeter.

P = 7 + 7 + 6 = 20 \text{ cm}

Explanation: Add all three sides.

Example 10: A wall is 8 m long and 3 m high. What is the area to be painted?

A = l \times w = 8 \times 3 = 24 \text{ m}^2

Explanation: Multiply the length and height.

Exercises

[WAEC] Find the perimeter of a square of side 11 cm. [Past Question]
Calculate the perimeter of a rectangle with length 18 cm and width 6 cm.
A triangle has sides 7 cm, 8 cm, and 10 cm. Find its perimeter.
[NECO] Find the area of a rectangle of length 9 m and width 7 m. [Past Question]
What is the area of a square whose perimeter is 32 cm?
[JAMB] Find the area of a triangle with base 12 cm and height 5 cm. [Past Question]
A square playground is 20 m long on each side. What is its area?
[NABTEC] A rectangle is 14 m long and 10 m wide. What is its perimeter? [Past Question]
Find the side of a square whose area is 64 cm².
Calculate the perimeter and area of a rectangle with length 22 cm and width 8 cm.

Conclusion/Recap

In this lesson, you’ve learned how to calculate perimeter and area of basic shapes such as squares, rectangles, and triangles. These skills help in practical tasks like measuring land or walls. Next, we will explore Volume and Surface Area.