Question

Find the area of shaded region ........​

Answer 1

Answer:

0.46128 cm²

Step-by-step explanation:

let the coordinates of the semicircle centre be (0,0) ,

it's equation is x² + y² = 7²                --------(A)

the coordinates of B is (7,0) and C is (-7,-7)

the equation of BC is y/x-7 = -7/-14 = 1/2 , y = 1/2(x-7) , substituting into (A)

(x-7)² + 4x² = 2².7²

5x²-2.7x -3.7²=0

x = 7 , -4.2

x = -4.2 , y = -5.6

the coordinates of point of intersection I = (-4.2 , -5.6)

length of chord ID = 1.4(5) = 7 cm.

sin∝/2 = 7/2÷7 = 1/2 , ∝/2 = 30° , ∝ = 60° = π/3

Area of sector = r²/2(∝ - sin∝) = 7²/2(π/3 -√3/2)

Area of Triangle ICD = 7/2(7 -5.6) = 7²/2(0.2)

SHADED AREA = 7²/2( 1/5 - π/3 + √3/2) cm²

                           = 0.46128 cm²