# Find the area of the shaded region in Fig. 12.21, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

**Solution:**

We use the concepts related to areas of squares and circles.

From figure it is clear that diameter of both semicircles = side of square = 14 cm

∴ Radius of each semicircle (r) = 14/2 = 7 cm

Visually, it is clear

Area of shaded region = Area of square ABCD - (Area of semicircle APD + Area of semicircle BPC)

= (side)^{2} - (πr^{2}/2 + πr^{2}/2)

= (side)^{2} - πr^{2}

Semicircles APD and BPC are drawn using sides AD and BC respectively as diameter.

∴ Diameter of each semicircle = 14 cm

Radius of each semicircle (r) = 14/2 = 7 cm

Area of shaded region = Area of square ABCD - (Area of semicircle APD + Area of semicircle BPC)

= (side)^{2} - (1/2πr^{2} + 1/2πr^{2})

= (14)^{2} - π × (7)^{2}

= 196 cm^{2} - 22/7 × 7 cm × 7 cm

= 196 cm^{2} - 154 cm^{2}

= 42 cm^{2}

**Video Solution:**

## Find the area of the shaded region in Fig. 12.21, if ABCD is a square of side 14 cm and APD and BPC are semicircles

### NCERT Solutions Class 10 Maths - Chapter 12 Exercise 12.3 Question 3

Find the area of the shaded region in Fig. 12.21, if ABCD is a square of side 14 cm and APD and BPC are semicircles

The area of the shaded region if ABCD is a square of side 14 cm and APD and BPC are semi-circles is 42 cm^{2}