Lesson 3: Length and Area of Plane Figures

📘 Introduction

Imagine you’re designing a farm, painting your bedroom wall, or even measuring a football pitch. You’ll need to know how long things are and how much space they cover. In mathematics, we call these measurements length and area.

This lesson will guide you through finding the perimeter (total length around a figure) and area (space inside a shape) of common plane figures like squares, rectangles, triangles, circles, and compound shapes.

🧠 Key Concepts and Explanations

1. What Are Plane Figures?

Plane figures are flat shapes that lie on a single surface. They include 2D shapes like squares, rectangles, triangles, parallelograms, and circles.

2. Perimeter (Length Around a Shape)

Perimeter is the total distance around the edge of a shape. You add up all the sides.

Shape	Perimeter Formula	Example
Square		Side = 6 cm → P = 24 cm
Rectangle		l = 8 cm, w = 5 cm → P = 26 cm
Circle		r = 7 cm → C ≈ 44 cm

Note: Use π = 3.14 unless told otherwise.

3. Area (Space Inside a Shape)

Area tells us how much surface a figure covers. We measure area in square units like cm² or m².

Shape	Area Formula	Example
Square		s = 5 cm → A = 25 cm²
Rectangle		l = 10 cm, w = 4 cm → A = 40 cm²
Triangle		b = 6 cm, h = 3 cm → A = 9 cm²
Circle		r = 4 cm → A ≈ 50.24 cm²

4. Compound Shapes

Sometimes, shapes are made by joining two or more basic shapes (e.g., a rectangle attached to a triangle). To find the area:

1. Break it into simple parts
2. Find the area of each part
3. Add them up

🧮 Sample Problem Walkthroughs

Example 1: Find the perimeter and area of a square with side 9 cm.

• Perimeter =
• Area =

Example 2: A rectangular field is 25 m long and 15 m wide. Find:

• Perimeter =
• Area =

Example 3: A compound shape consists of a rectangle (6 cm by 4 cm) and a triangle on top (base 6 cm, height 3 cm).

• Area of rectangle =
• Area of triangle =
• Total area = 24 + 9 = 33 cm²

✏️ Practice Exercises

Section A: Direct Calculation

1. A rectangle is 12 cm long and 7 cm wide. Find its perimeter and area.
2. Find the area of a triangle with base 10 cm and height 6 cm.
3. A circular garden has a radius of 5 m. Calculate its area.

Section B: Word Problems

4. A square tile has an area of 64 cm². What is the length of one side?
5. Kwame wants to put a fence around his rectangular farm, 20 m by 15 m. How much fencing will he need?
6. A floor is shaped like a rectangle with a semicircle at one end. The rectangle is 8 m long and 6 m wide; the semicircle has radius 3 m. Find the total area of the floor. (Use π = 3.14)

📝 Answers & Explanations

• Q1: Perimeter = 38 cm, Area = 84 cm²
• Q2: A = 30 cm²
• Q3: A =
• Q4: Side =
• Q5: Perimeter = 2(20 + 15) = 70 m
• Q6: Rectangle A = 48 m², Semicircle A = (1/2 × π × 3²) = 14.13 m². Total = 62.13 m²

🔁 Recap

• Perimeter is the length around a shape
• Area is the surface inside a shape
• Each shape has its own formula — memorize and apply them
• For compound shapes, break into parts and sum areas

🪞Reflection Prompt

Where might you use perimeter and area in real life? Try measuring the walls, garden, or school compound around you. What do you notice about the shapes and how they’re combined?