Answer:
96 cm²
Step-by-step explanation:
From the question,
s = (2πr∅/360)+2r................. Equation 1
Where s = Perimeter of a sector, r = radius, ∅ = angle subtend by the sector at the center of the circle.
Given: s = 40 cm, r = 8 cm
Constant : π = 3.14.
Substitute into equation 1 and solve for ∅
40 = (2×8×3.14×∅/360)+(2×8)
40 = (50.24∅/360)+16
40-16 = 50.24∅/360
50.24∅/360 = 24
50.24∅ = 24×360
50.24∅ = 8640
∅ = 8640/50.24
∅ = 171.97°
Area of a sector (A') = ∅πr²/360
A' = 171.97×3.14×8²/360
A' = 95.997
A' ≈ 96 cm²
