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# Which explanation justifies how the area of a sector of a circle is derived?

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Which explanation justifies how the area of a sector of a circle is derived?

1. Determine how many triangles can fit into a circle. Divide 360dg by the number of triangles. Multiply the quotient by the area of the circle.

2. Determine the degree of the sector. Divide by 180dg and then multiply it by the area of the triangle the sector is in.

3. Partition the circle into unit squares. Determine the are of the sector and multiply the area by the degree of the circle.

4. Calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360dg to get a fraction. Multiply the area of the circle by this fraction.

Guest Mar 21, 2017
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$$\frac{\text{central angle of sector}}{\text{360 degrees}}=\frac{\text{area of sector}}{\text{area of circle}}$$

I believe the correct explanation is number 4.

hectictar  Mar 22, 2017

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