DEFINITION

The area of a plane shape is the amount of surface enclosed within its boundary. It is measured in square units (cm², m², etc.).

A regular plane shape is a polygon or closed figure whose sides and angles are all equal (e.g. square, equilateral triangle, regular hexagon). However, in JSS1 we often study common shapes like: square, rectangle, triangle, parallelogram, trapezium, and circle.

FORMULAE FOR AREAS

1. Square

• Area (A) = side × side = s².

+------+
|      |
|      |   Area = s × s
+------+
  

2. Rectangle

• Area (A) = length × breadth = l × b.

+----------+
|          |
|          |   Area = l × b
+----------+
  

3. Triangle

• Area (A) = ½ × base × height = ½ × b × h.

   /\
  /  \      Area = ½ × base × height
 /____\
  

4. Parallelogram

• Area (A) = base × height = b × h.

  /------/
 /      /   Area = base × height
/------/
  

5. Trapezium

• Area (A) = ½ × (sum of parallel sides) × height = ½ × (a + b) × h.

   +------+
  /        \    Area = ½ × (a + b) × h
 +----------+
  

6. Circle

• Area (A) = πr².

   ****
 *      *
*        *   Area = π × r × r
 *      *
   ****
  

(r = radius)

WORKED EXAMPLES

Example 1: Square

Find the area of a square of side 12 cm.

Solution:
A = s²
= 12 × 12
= 144 cm²

Answer: 144 cm²

Example 2: Rectangle

Find the area of a rectangle with length 18 cm and breadth 12 cm.

Solution:
A = l × b
= 18 × 12
= 216 cm²

Answer: 216 cm²

Example 3: Triangle

Find the area of a triangle whose base is 14 cm and height is 10 cm.

Solution:
A = ½ × b × h
= ½ × 14 × 10
= 7 × 10
= 70 cm²

Answer: 70 cm²

Example 4: Parallelogram

The base of a parallelogram is 20 cm and the height is 8 cm. Find its area.

Solution:
A = b × h
= 20 × 8
= 160 cm²

Answer: 160 cm²

Example 5: Trapezium

The parallel sides of a trapezium are 10 cm and 14 cm, and its height is 6 cm. Find its area.

Solution:
A = ½ × (a + b) × h
= ½ × (10 + 14) × 6
= ½ × 24 × 6
= 12 × 6
= 72 cm²

Answer: 72 cm²

Example 6: Circle

Find the area of a circle of radius 7 cm. Take π = 22/7.

Solution:
A = πr²
= (22/7) × 7 × 7
= 22 × 7
= 154 cm²

Answer: 154 cm²

SUMMARY

• Area is the surface enclosed within a plane shape.


• Units are square units (cm², m², etc.).


• Formulas to remember:


• Square → A = s²


• Rectangle → A = l × b


• Triangle → A = ½ × b × h


• Parallelogram → A = b × h


• Trapezium → A = ½(a + b) × h


• Circle → A = πr²