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Question:
Find the area of the shaded segment. Round your answer to the nearest square centimeter.
a) 24 cm²
b) 23 cm²
c) 21 cm²
d) 22 cm²
Answer:
d) 22 cm²
Explanation:
We have Area and a Triangle in that diagram.
In other to find the shades segment , we have to find the Area of the triangle and the Area of the sector
Step 1
Area of a Triangle
= 1/2 × a × b × sin θ
Where θ = 120°
a = 6 cm
b = 6 cm
Area of the triangle = 1/2 × 6 × 6 × sin 120°
= 15.59 cm²
Step 2
Area of the sector
The formula is given as
Area = πr²θ/360
r = radius = 6cm
Area = π × 6² × 120/ 360
Area = 37.699111843cm²
Approximately = 37.70 cm²
Step 3
The Area of the shaded segment = Area of the sector - Area of the triangle
= 37.70cm² - 15.59cm²
= 22.11 cm²
Approximately to the nearest square centimeter
= 22 cm²