Question

In Fig. , PQRS is a square of side 4 cm. Find the area of the shaded square.

Answer 1

Side of square = 4cm
radius of quadrant = 1cm
radius of circle = 1 cm
area of shaded region = area of square - (area of 4 quadrants+ area of a circle)

$=(side{)}^2-(4\times \frac{90}{360}\times \frac{22}{7}\times 1\times 1+\frac{22}{7}\times 1\times 1)$

$=(4\times 4)-(\frac{22}{7}+\frac{22}{7})$

$=16-\frac{44}{7}$

$=\frac{112-44}{7}=\frac{68}{7}c{m}^2$

detailed solution

Each quadrant is a sector of 90° in a circle of 1 cm radius

$=\frac{{90}^0}{{360}^0}\pi r^2$

Area of each quadrant

$=\frac{1}{4}\times \frac{22}{7}\times (1{)}^2=\frac{22}{28}c{m}^2$

Area of square $=(side{)}^2=(4{)}^2=16c{m}^2$

Area of circle $=\pi r^2=\pi (1{)}^2=\frac{22}{7}c{m}^2$

Area of the shaded region = Area of square − Area of circle − 4 $times$ Area of quadrant

$=16-\frac{22}{7}-4\times \frac{22}{28}$

$=16-\frac{22}{7}-\frac{22}{7}$

$=16-\frac{44}{7}=\frac{112-44}{7}=\frac{68}{7}c{m}^2$