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

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.

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.

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

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

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

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°.