Find the area of pentagon $P Q R S T$ in which $Q D ⊥ P R, R E ⊥ P S$ and $T F ⊥ P S$ such that $P R = 10$ cm, $P S = 12$ cm, $Q D = 3$ cm, $R E = 7$ cm and $T F = 5$ cm.

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Solution

Area of pentagon $P Q R S T$
Area of $△ P S T +$ Area of $△ P R S +$ Area of $△ P Q R$
$= \frac{1}{2} \times 5 \times 12 +$ $\frac{1}{2} \times 7 \times 12 +$ $\frac{1}{2} \times 3 \times 10$
$= 30 + 42 + 15 = 87$

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= 6.5

= 5.5

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