Answer:
23.3285 in²
Step-by-step explanation:
From the above diagram, we can see that the shaded portion is a circular in shape. The shaded portion is coming together of two segments of two circles
The formula for the area of the segment is given as:
A = (½) × r² × [(π/180) θ – sin θ]
Where,
r: radius of the circle
θ = angle
a) Circle 1: the largest circle:
A = (½) × r² × [(π/180) θ – sin θ]
r: radius of the circle = 10 inches
θ = angle = 60°
A = (½) × 10² × [(π/180) × 60° – sin 60]
A = 9.0586 in²
b) Circle 2: the smallest circle:
A = (½) × r² × [(π/180) θ – sin θ]
r: radius of the circle = √50 inches
θ = angle = 90°
A = (½) × (√50) ² × [(π/180) × 90° – sin 90]
A = 14.2699 in²
Total area of the shaded portion:
Area of the segment of the large circle + Area of the segment of the small circle
A = 9.0586 in² + 14.2699 in²
A = 23.3285 in²
