detailed solution

Correct option is A

Let us given that,

ABCD is a square of side 14 cm and here 4 circles are formed.

Since the circles are touching each other extremely.

Consider, the radius of each circle is r

and ABCD is a square so each angle is 90⁰.

So, the angles and radii for all sectors are equal.

We know that, the formula for the area of the sector of a circle.

Area of the sector = $\frac{\theta }{{360}^0}$ $\times$ ${\mathrm{\pi r}}^2$

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

= ${\mathrm{\pi r}}^2$/4 cm²

Radius = 14/2 = 7 cm

Area of each sector = 1/4 $\times$ 22/7 $\times$ 7 $\times$7 

= 77/2 cm²

Area of shaded region = Area of square $-$ 4 $\times$ Area of each sector

= (14)² $-$ 4 $\times$77/2 

= 196 $-$ 154 

= 42 cm²

detailed solution

Correct answer is 1

Let us given that,

ABCD is a square of side 14 cm and here 4 circles are formed.

Since the circles are touching each other extremely.

Consider, the radius of each circle is r

and ABCD is a square so each angle is 90⁰.

So, the angles and radii for all sectors are equal.

We know that, the formula for the area of the sector of a circle.

Area of the sector = $\frac{\theta }{{360}^0}$ $\times$ ${\mathrm{\pi r}}^2$

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

= ${\mathrm{\pi r}}^2$/4 cm²

Radius = 14/2 = 7 cm

Area of each sector = 1/4 $\times$ 22/7 $\times$ 7 $\times$7 

= 77/2 cm²

Area of shaded region = Area of square $-$ 4 $\times$ Area of each sector

= (14)² $-$ 4 $\times$77/2 

= 196 $-$ 154 

= 42 cm²