Find the area of the field shown in the figure by dividing it into a square rectangle and a trapezium.

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Solution

Produce EF to H to meet AB at H and draw DK || EH

$∴ H F = 4 c m, K D = H E = 4 + 4 = 8 c m H K = E D = 4 c m, K B = 12 - (8) = 4 c m N o w a r e a o f s q u a r e A G F H = 4 \times 4 = 16 c m^{2} a r e a o f r e c t a n g l e K D E H = l \times b = 8 \times 4 = 32 c m^{2} A n d a r e a o f t r a p e z i u m B C D K . = \frac{1}{2} (B C + K D) \times B K = \frac{1}{2} (3 + 8) \times 4 c m^{2} = \frac{1}{2} \times 11 \times 4 = 22 c m^{2} ∴ T o t a l a r e a o f t h e f i g u r e = 16 + 32 + 22 = 70 c m^{2} .$

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