Page 234 - MathGPT_V1.0_C5

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AREA OF A COMPOSITE FIGURE

Example 1: Find the area of the following figure.
5 cm 1 cm

1 cm 3 cm

Solution: The given figure can be divided into three rectangles as 5 cm 1 cm
shown in the figure below. (I)
Area of rectangle (I) = 5 cm × 1 cm = 5 sq. cm
1 cm
Area of rectangle (II) = 3 cm × 1 cm = 3 sq. cm (II) 3 cm
Area of rectangle (III) = 5 cm × 1 cm = 5 sq. cm
Area of the complete figure (III)

= area of rectangle (I) + area of rectangle (II) + area of rectangle (III)
= 5 sq. cm + 3 sq. cm + 5 sq. cm = 13 sq. cm

Example 2: Find the area of the following figure.

6 cm 8 cm
10 cm 12 cm 8 cm

24 cm
Solution: We divide the given figure in rectangles and square.

Area of rectangle A = 10 cm × 4 cm = 40 sq. cm
Area of rectangle B = 12 cm × 4 cm 4 cm

= 48 sq. cm 6 cm 8 cm
Now, area of square C = 8 cm × 8 cm 10 cm A 12 cm
= 64 sq. cm 4 cm B C 8 cm

Thus, the area of the given shape 24 cm
= Area of square C + Area of rectangle B + Area of rectangle A

= (64 + 48 + 40) sq. cm = 152 sq. cm.

AREA OF A TRIANGLE

Look at the square shown alongside.
Area of the square = 6 cm × 6 cm = 36 sq. cm 6 cm

A diagonal divides a square into two halves. Each half is a triangle.
Thus, the area of a triangle is half the area of the square. 6 cm

232 Mathematics-5