a. The area of the sector is 72.0472 cm²
b. The area of the shaded region is 43.1785 cm²
To solve the question, we need to find the area of the shaded portion.
How to find the area of the shaded portion?
The area of the shaded portion, A = area of sector A' - area of triangle, A"
a. The Area of sector
Area of sector A = Ф/360 × πr² where
- Ф = angle of sector = 129° and
- r = radius of circle = 8 cm
So, A = Ф/360 × πr²
A = 129/360 × π(8 cm)²
A = 129/360 × 64πcm²
A = 8256π/360 cm²
A = 22.93333π cm²
A = 72.0472 cm²
So, the area of the sector is 72.0472 cm²
The Area of triangle
Area of triangle, A" = 1/2r²sinФ where
- r = radius of circle = 8 cm and
- Ф = angle of sector = 129°
So, A" = 1/2r²sinФ
A" = 1/2 × (8 cm)²× sin129°
A" = 1/2 × 64cm² × 0.7771
A" = 32 cm² × 0.7771
A" = 28.8687 cm²
b. The Area of the shaded region
The area of the shaded region A = area of sector A' - area of triangle, A"
= 72.0472 cm² - 28.8687 cm²
= 43.1785 cm²
So, the area of the shaded region is 43.1785 cm²
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