Question

ABCD is a square of area $153.76c{m}^2$. Find the area of the shaded part if P, Q, R, S are the midpoints of the sides.

Answer 1

Area of the square $=side\times side=153.76c{m}^2$
$\Rightarrow$ side = 12.4 cm
[Formula]

Area of the shaded region APQCRS = area of the square ABCD - area of the triangle PBQ - area of the triangle DSR

Area of the triangle $PBQ=\frac{1}{2}\times (6.20\times 6.20)=19.22c{m}^2$
[Since P and Q are the mid-points of the sides AB and BC]

Area of the triangle $DSR=\frac{1}{2}\times (6.20\times 6.20)=19.22c{m}^2$
[Since S and R are the mid-points of the sides AD and DC]

So, Area of the shaded region $=153.76-19.22-19.22=115.32c{m}^2$
[Substitute and simplify]