Remember, the area of a circle is πr2{\displaystyle \pi r^{2}}. When finding the area of a sector, you are really just calculating the area of the whole circle, and then multiplying by the fraction of the circle the sector represents. A circle is 360 degrees, so when you place the measurement of the sector’s central angle over 360, it gives you the fraction of the whole circle. [2] X Research source
For example, if the central angle is 100 degrees, you will divide 100 by 360, to get 0. 28. (The area of the sector is about 28 percent of the area of the whole circle. ) If you don’t know the measurement of the central angle, but you know what fraction of the circle the sector is, determine the measurement of the angle by multiplying that fraction by 360. For example, if you know the sector is one-fourth of the circle, multiply 360 by one-fourth (. 25) to get 90 degrees.
For example, if the radius is 5 cm, you will square 5 to get 25, and then multiply 25 by 3. 14, to get 78. 5. If you don’t know the length of the radius, but you know the diameter, simply divide the diameter by 2 to find the radius.
For example, 0. 28 x 78. 5 = 21. 89. Since you are finding the area, the answer will be in square centimetres.
Remember the formula for finding the circumference (perimeter) of a circle is 2𝝅r. If you know the length of the arc (which is a portion of the circumference), you can find what fraction of the circle the sector represents by comparing the arc length to the total circumference. The complete formula would be A=(l2πr)πr2{\displaystyle A=\left({\frac {l}{2\pi r}}\right)\pi r^{2}}, but you can simplify it to A=rl2{\displaystyle A={\frac {rl}{2}}}. [5] X Research source
For example, if the arc length is 5 cm and the radius is 8 cm, your new numerator will be 40.
For example, 402=20{\displaystyle {\frac {40}{2}}=20}. Since you are finding the area, your answer will be in square centimetres.
