Question

Two circular flower beds have been shown on two sides of a square lawn $ABCD$ of side $56$ m. If the center of each circular flower bed is the point of intersection $O$ of the diagonals of the square lawn, find the sum of the areas of the lawn and the flower beds.

Answer 1

Refer Image

$x=\frac{1}{2}56\sqrt{2}$ ..... radius OB

$=28\sqrt{2}cm$

Area of 1 shaded region = $\frac{1}{4}(\pi \times (28\sqrt{2}{)}^2-56\times 56)$

$=448c{m}^2$

$\therefore$ total area = area of square + two shaded region

$=56\times 56+2\times 448$

$=4032m^2$