3.3 AREA
Area is defined as the measure of surface. The international standard unit (SI) of area is square metre (m2). Other units are hectares and acres.
NOTE:
1 hectare = 1 hectometre × hectometre
1 hectare = 100 metres × 100 metres
1 hectare = 10 000 m2
NOTE:
1 acre = 4046 m2
3.3.1 AREA OF PLANE FIGURES
RECTANGLES
Area of a rectangle is the product of the base length and its height.
A = l × w
Example 3.10
A rectangle whose length is 8 metres has an area of 32 square metres. Calculate the width.
Solution:
Let the width be x
A = l × w
32 = 8x
x = 4 metres
Example 3.11
The length of a rectangular flower lawn is 24 m. If its diagonal is 25 m, calculate the area.
Solution:
x2 + 242 = 252
x2 + 576 = 625
x2 = 49
x = 7 m
A = 24 × 7 = 168 m2
PARALLELOGRAM
A parallelogram is a four sided figure in which opposite sides are equal and parallel.
A = base × height
Example 3.12
Calculate the area of the parallelogram drawn below.A = b × h
A = 8 cm × 5 cm
A = 40 cm2
RHOMBUS
A rhombus is a special parallelogram with all sides equal.
Example 3.13
A rhombus has its diagonals measuring 12 cm and 20 cm. Calculate the area of the rhombus.
A = 1/2 × 12 × 20
A = 120 cm2
TRAPEZIUM
A trapezium is a four sided figure in which two sides are parallel.
Example 3.14
Find the area of the trapezium shown below.
A = (10 + 8) 2 × 5
A = 45 cm2
CIRCLES
A = πr2 where r is the radius of the circle.
Example 3.15
A circle has a diameter of 70 m, calculate the area of the circle.
A = 22/7 × 35 × 35
A = 3850 m2
Example 3.16
Find the radius of a circle which has an area of 154 cm².
154 = 22 7 r2
r = 7 cm
3.3.2 AREA OF BORDERS AND COMBINED SHAPES
Example 3.17
The figure below shows a flower bed surrounded by a path. Calculate the area of the path.
A = 58 m2
Exercise 3.3
1. A parallelogram has a base of 5 cm and a height of 3 cm. Find the area.
cm²2. The area of a rectangular plot is 1 hectare. Width = 80 m. Find the length.
mLength = 10,000 ÷ 80 = 125 m
3. Find the area of a circle whose radius is 7 cm.
cm²4. The diameter of a circle is 42 m. Calculate its area.
m²A = 22/7 × 21 × 21 = 1386 m²
5. Rectangle 500 m by 250 m. Find area in hectares.
hectares= 12.5 hectares
6. Find the length marked x if base = 6 cm and area = 96 cm².
cm96 = 6 × x
x = 16 cm
7. Find the area of the shaded portion.
cm²A = Area of square − Area of circles
A = 14 × 14 − 4 × (22/7 × 3.5 × 3.5)
A = 42 cm²
8. A wire 40 cm is folded to form a square. Find its area.
cm²Side = 40 ÷ 4 = 10
Area = 10 × 10 = 100 cm²
9. 200 students each get cloth 20 cm by 25 cm. Rate = Ksh 200 per m². Find total cost.
Ksh= 0.05 m²
Total area = 200 × 0.05 = 10 m²
Cost = 10 × 200 = Ksh 2000
10. Out of a rectangular sheet of paper, a strip is cut out as shown below. Find the area of the remaining portion.
cm²Dimensions of the cut part are 20 cm by 15 cm.
A = Area of the bigger rectangle − Area of the cut rectangle
A = (25 × 20) − (20 × 15)
A = 200 cm²