Question

Find the area of the shaded portion in the following figure :

Answer 1

Given in fig$.$

$SR=10+10=20cm$

$QR=20cm$

$TS=10cm$

So$,$

$PT=10cm$

$PQ=20cm$

As we can see that $PQRS$ is square

So$,$

Area of PQRS $=20\times 20$

$=400cm²$

Area of triangle $QRU=1/2\times 10\times 20$

$=100cm²$

Area of triangle $TSU=1/2\times 10\times 10$

$=50cm²$

Area of triangle $QPT=1/2\times 10\times 20$

$=100cm²$

Now$,$

Area of shaded region = Area of square -$($Area of triangle QRU + Area of triangle $TSU$ $+$ Area of triangle $QPT$ $)$

$=400-(100+50+100)$

$=400-250$

$=150cm²$

So$,$

Area of shaded portion $=150cm²$