Find the area of a sector of a semicircle?

how would i go about finding the area of a sector in a semicircle? do i make the angle measure double and then put it over 360 or would i keep it and put it over 180 and still multiply that fraction by pi*radius squared?

1 Answer

  • 4 years ago
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    Both approaches lead to the same wrong answer. If you double and divide by 360, that's exactly the same as keeping it undoubled and dividing by 180.

    What you really need to do is divide the angle by 180, giving you the fraction of the semicircle that the sector takes up. Then multiply by ONE-HALF pi*(radius^2), since that's the area of the whole semicircle. That is, half of a circle's area.

    The other option is to divide the angle by 360, without doubling. This will give you the fraction of a whole circle that the angle takes up, so you can multiply by pi*(radius^2), the area of a whole circle.

    The two approaches you suggested would give you twice the area.

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