Question

In Fig. 19.41, AE = 28 cm, AK = 8 cm and AB = CD = DE = FG = HI = IJ = 5 cm. Calculate the
total area of the shaded region.
5 cm
K, J
G - F
8 cm
А В
C D E
28 cm​

Answer 1

Answer:

Radius of larger circle,(OA) R = 7 cm

Diameter of smaller circle,(OD) = 7 cm

Radius of smaller  circle = 7/2 cm

Height of ΔBCA( OC) = 7 cm

Base of ΔBCA ( AB )= 14 cm

Area of ΔBCA = 1/2 × base × height

Area of ΔBCA = 1/2 × AB × OC = 1/2 × 7 × 14 = 49 cm²

Area of larger semicircle with radius (OA)7 cm = 1/2 ×π ×7²= 1/2 ×22/7 ×7×7 = 77 cm²

Area of smaller circle with radius 7/2 cm = πr²= 22/7 × 7/2 × 7/2 = 77/2 cm²  

Area of the shaded region =Area of smaller circle with radius 7/2 cm +Area of larger semicircle with radius 7 cm - Area of ΔBCA  

Area of the shaded region = 77/2 + 77 - 49= 77/2 + 28 = (77 +56) /2= 133/2

Area of the shaded region = 66.5 cm²

Step-by-step explanation: