Finding Sector Area

Definition: The area of a sector of a circle can be calculated using degrees or radians.

Sector area of a circle in radians:
Sector Area = 1/2 * θ * r²

Sector area of a circle in degrees:
Sector Area = θ / 360 * π * r²

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Example: Find the area of a sector with a radius of 7 cm and a central angle measure of 100°. Round to the nearest tenth.

Solution:

Use the sector area formula and the information provided to find the area of the sector.

Step 1: Read and gather important information from the word problem. From this question we know:
radius = 7 cm
central angle = 100°

Step 2: Recall the sector area formula and plug the given information into the equation. We are working in degrees, so will use the following formula:
Sector Area = θ / 360 * π * r²
= 100 / 360 * π * 7²
= 0.277 * π * 49
= 42.76

Since we are measuing area, we will use square units:

Sector Area = 42.8 cm²

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