Question

I given figure ABCD is a rectangle. the radius of the semicircles drawn on AD and BC as diameters and radius of circle drawn in between is the same. if BC = 7 cm, find the area of the shaded region


please give an appropriate answer​

Answer 1

Answer:

Step-by-step explanation:

Given:

Length of a rectangle (AB) = DC = 14 cm

Breadth of a rectangle( BC) = AD=7 cm

AREA OF SEMICIRCLE with DIAMETER DC= 1/2πr² = ½(22/7) × (14/2)²

= 11 × 7 = 77 cm²

AREA OF RECTANGLE (ABCD) = Length × Breadth = AB × DC = 14 × 7 = 98 cm²

AREA OF 2 SEMI CIRCLE with DIAMETER BC & AD= 2× 1/2πr² =(22/7) × (7/2)² = 11 ×7 / 2

= 77 /2 cm²

AREA OF SHADED REGION = Area of rectangle ABCD -  area of semicircle with diameter DC + Area of 2 semicircle with diameter  BC and AD

Area of shaded region = 98 - 77 + 77/2

= 21 +  77/2 = (42 +77)/2 = 119/2 = 59.5 cm²

Area of shaded region = 59.5 cm²