Question

In Fig. 4, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square as diameter Find the area 22 of the shaded region. (use $(\pi =\frac{22}{7} )$ )

Answer 1

Refer to the attachment please.

Answer 2

Answer:

84 cm²

Step-by-step explanation:

From the figure, we can conclude that:

⇒ A = B = C = D

⇒ Diameter of the semi circle = 14 cm

Find the radius:

Radius = Diameter ÷ 2

Radius = 14 ÷ 2 = 7 cm

Define the centre of the square:

Let the centre of the square be "o"

Find the area of the semicircle AOB:

Area AOB = 1/2 (πr²)

Area AOB = 1/2 ((22/7)(7)²) = 77 cm²

Find the area of the semicircle COD:

Area ODC =Area AOB

Area COD = 77 cm²

Find area of the square:

Area of the square = Length²

Area of the square = 14² = 196 cm²

Find the area B and D:

Area B + D = Area of square - Semicircle AOB - Semi Circle COD

Area B + D = 196 - 77 - 77 = 42 cm²

Find the area A + B + C + D:

Area = 2 x 42 = 84 cm²

Answer: 84 cm²