In the following figure, find the area of the shaded portion.

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Solution

Here, $S R = S U + U R = 10 + 10 = 20$ cm, $Q R = 20$ cm
$P Q = S R = 20$ cm, $P T = P S - T S = 20 - 10$ cm
$T S = 10$ cm, $S U = 10$ cm, $Q R = 20$ cm and $U R = 10$ cm
Area of shaded region $=$ Area of square PQRS $-$ Area of $Δ$ QPT $-$ Area of $Δ$ TSU $-$ Area of $Δ$ UQR
$= (S R \times Q R) - \frac{1}{2} \times P Q \times P T - \frac{1}{2} \times S T \times S U - \frac{1}{2}$
$= 20 \times 20 - \frac{1}{2} \times 20 \times 10 - \frac{1}{2} \times 10 \times 10 - \frac{1}{2} \times 20 \times 10$
$= 400 - 100 - 50 - 100 = 150 c m^{2}$ .

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