Question

Semicircles are described on the sides of the rectangle
ABCD. Given that AB = 2BC = 7 cm, calculate
(i) the perimeter.
(ii) the area of the shaded portion.




Plzz give correct answer​

Answer 1

(I) perimeter = Perimeter of big circle + Perimeter of small circle

(two semicircles will form a complete circle)

Radius of big semicircle = 7/2 cm

Radius of small. semicircle = 7/4 cm

= 2π7/2+2π7/4

= 2π(7/2+7/4)

= 2π(21/4)

$= 2 \times \frac{22}{7} \times \frac{21}{4}$

= 33 cm

(ii)

Area of shaded portion = Area of small semicircle + area of big semicircle + area of rectangle

= π(7/4)^2+π(7/2)^2+(7/2)(7/4)

= π(49/16 + 49/4)+49/8

= π(245/16)+49/8

= 22/7 × 245/16 + 49/8

= 385/8 + 49/8

= 435/8 cm ^2