# Calculate the area of the designed region in Fig. 12.34 common between the two quadrants of circles of radius 8 cm each

**Solution:**

We use the formula for the area of sectors of the circle and the area of the square to solve the problem.

In a circle with radius r and the angle at the centre with degree measure θ, we know Area of each sector = θ/360° × πr^{2}

Area of the quadrant = 90°/360° × πr^{2} = 1/4 πr^{2}

Area of plain part in square = Area of square - Area of quadrant

= side^{2} - (1/4 × πr^{2})

= (8 cm × 8 cm) - (1/4 × 22/7 × 8 cm × 8 cm)

= 64 cm^{2} - 352/7 cm^{2}

= 96/7 cm^{2}

Area of the designed region = Area of the quadrant - Area of plain part in square

= (1/4 × 22/7 × 8 cm × 8 cm) - 96/7 cm^{2}

= 352/7 cm^{2} - 96/7 cm^{2}

= 256/7 cm^{2}

**Video Solution:**

## Calculate the area of the designed region in Fig. 12.34 common between the two quadrants of circles of radius 8 cm each

### NCERT Solutions Class 10 Maths - Chapter 12 Exercise 12.3 Question 16:

Calculate the area of the designed region in Fig. 12.34 common between the two quadrants of circles of radius 8 cm each

The area of the designed region common between the two quadrants of circles of radius 8 cm each is 256/7 cm^{2}