Find the area of the trapezium PQRS.

$115 m^{2}$

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$110 m^{2}$

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$100 m^{2}$

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$114 m^{2}$

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Solution

The correct option is D
$114 m^{2}$

From the figure, it is clear that
ST = PS - PT
= 12 m - 7 m = 5 m
Now from right triangle RTS, we have $R S^{2} = R T^{2} + S T^{2}$
$\Rightarrow R T^{2} = R S^{2} - S T^{2} = (13)^{2} - (5)^{2}$
$∴ R T^{2} = 169 - 25 = 144$
$\Rightarrow R T = \sqrt{144} = 12 m$
Now, area of trapezium PQRS
$= \frac{1}{2} (P S + Q R) \times R T$
$= \frac{1}{2} (12 m + 7 m) \times 12 m$
$= \frac{1}{2} \times 19 m \times 12 m$
$= \frac{1}{2} \times 228 m^{2} = 114 m^{2}$

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