Question

In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square where O and O' are centres of the circles. Find the area of shaded region.​

Answer 1

Answer:

The area of shaded region is 1708 cm².

Step-by-step explanation:

Given :

Side of a square = 28 cm

Radius of circle = half of the length of the side of a square

Radius of circle,r  = ½ × side of a square

r = ½ × 28  

r = 14 cm

Radius of circle = 14 cm

Area of shaded region , A = Area of a square + Area of two circles - Area of two quadrants

A = side² + 2 × πr² - 2 × ¼ πr²

A = side² + (2 × πr² - ½  πr²)

A = side² + (4πr² - 1πr²)/2

A = side² + 3πr²/2

A = 28² + 3 × 22/7 × 14² × ½

A = 28² + 3 × 11 × 2 × 14

A = 784 + 924

A = 1708 cm²

Area of shaded region = 1708 cm²

Hence, the area of shaded region is 1708 cm².

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Answer 2

$\huge\mathfrak\blue {Solution}$

It is given that the side of square is 28 cm .

And the radius of each circle is 1/2 of the side of square .

Then ,

Radius (r) = 1/2 × 28

r = 14 cm

Now ,

Area of shaded region = Area of square + Area of 2 circles - Area of 2 quadrants .

$= {side}^{2} + 2 \times \pi {r}^{2} - 2 × \frac{1}{4} \pi {r}^{2}$

$= {28}^{2} + (2 \times \frac{22}{7} \times 14 \times 14 )- ( \frac{1}{2} \times \frac{22}{7} \times 14 \times 14)$

$= 784 + (44 \times 2 \times 14) - (22 \times 14)$

$= 784 + (1232 - 308)$

$= 784 + 924$

$= 1708$

Hence , area of the shaded region is 1708 cm^2