Q&A for How to Calculate the Area of a Sector

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How do I find the area of a sector if I know the diameter and the arc length?

Donagan

Top Answerer

Divide the diameter by 2. That gives you the radius. Multiply the radius by the arc length, then divide by 2 again. That gives you the sector area.

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Question

How do I find the angle of a sector if I have arch length and radius?

Donagan

Top Answerer

Double the radius, then multiply by pi. That gives you the circumference. Divide the length of the arc by the length of the circumference. That gives you the fraction of the circumference represented by the arc. Multiply that fraction by 360°. That gives you the central angle of the sector.

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Question

What is the area of a sector bounded by an arc of 60 degrees with a radius of 3 feet?

Donagan

Top Answerer

As shown above, the formula is (60°/360°) π (3)² = (1/6)(3.14159)(9). The area will be expressed in square feet.

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How do I find the area of a segment that does not have degrees?

Donagan

Top Answerer

As indicated above, if you don't know the central angle, you have to know the radius and the arc length.

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Question

How do I find the area if I only know the radius?

Donagan

Top Answerer

You don't. The only two ways of finding a sector's area are shown above.

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Question

What is the central angle if the radius is 7 cm and the area of a sector is 15 cm squared?

Donagan

Top Answerer

As shown in Method 1 above, the sector area equals the central angle divided by 360° and then multiplied by πr². Therefore, the central angle is equal to the sector area multiplied by 360° and then divided by πr². In this case the angle is [(15 cm²)(360°)] / [(3.14)(7² cm²)] = 35.1°.

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