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Question 18

In the adjoining figure, two rectangles and two right-angled triangles are arranged as shown. The numbers shown inside each are their respective areas. Then the area of $$A$$ is

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Correct Answer: 48

Solution

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Let the left and right widths be $$w_1,w_2$$ and the upper and lower heights be $$h_1,h_2$$.

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The areas of the regions are as follows

$$w_1h_1=72$$, $$\dfrac{1}{2}w_2h_1=48$$ and $$w_2h_2=128$$. 

Hence $$w_1h_2=\dfrac{(w_1h_1)(w_2h_2)}{w_2h_1}=\dfrac{72 \times 128}{96}=96$$. 

Therefore, $$A=\dfrac{1}{2}w_1h_2=48$$.

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