Question

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

Answer 1

Here, $$SR=SU+UR=10+10=20$$cm, $$QR=20$$cm
$$PQ=SR=20$$cm, $$PT=PS-TS=20-10$$cm
$$TS=10$$cm, $$SU=10$$cm, $$QR=20$$cm and $$UR=10$$cm
Area of shaded region $$=$$Area of square PQRS$$-$$Area of $$\Delta$$QPT$$-$$Area of $$\Delta$$TSU$$-$$Area of $$\Delta$$UQR
$$=(SR\times QR)-\dfrac{1}{2}\times PQ\times PT-\dfrac{1}{2}\times ST\times SU-\dfrac{1}{2}$$
$$=20\times 20-\dfrac{1}{2}\times 20\times 10-\dfrac{1}{2}\times 10\times 10-\dfrac{1}{2}\times 20\times 10$$
$$=400-100-50-100=150cm^2$$.