Question

In the following figure, PQRS is square lawn with side $PQ=42$ meters. Two semi-circular flower beds are there on the sides PS and QR with center at O, the intersections of its diagonals. Find the total area of the two flower beds (shaded parts).

Answer 1

Given 2 shapes: Square and semicircle

The circle is cut in half to form a semi-circle. The square is placed between the two semi-circles.

Two semi-circles are the shaded part.

We will find the area of the shaded part which forms 1 circle.

Area of a circle = $\pi r^2$

The side of the square lawn serves as the diameter of the circle. Radius is half of the diameter.

$r=\frac{d}{2}=\frac{42}{2}=21m$

Area of circle = $3.14\times (21{)}^2=3.14\times 441=1384.74m^2$

The area of the shaded parts is $1,384.74$ square meters.