Discussion

Question:

Two sides of a plot measure 32 metres and 24 metres and the angle between them is a perfect right angle. The other two sides measure 25 metres each and the other three are not right angles.

What is the area of the plot?

Explanation:

$A C = \sqrt{24^{2} + 23^{2}} = 40$

Let us draw DE, which is perpendicular to AC.

Since ΔADC is isosceles, therefore DE will be its median and altitude both.

∴ DE = $\sqrt{25^{2} - 20^{2}} = 15$

∴ Required area = $(\frac{1}{2} \times 24 \times 32) + (\frac{1}{2} \times 40 \times 15)$ = 384 + 300 = 684

Hence, option (d).

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