An arc is a curved area of a circle that makes up part of its circumference. If you know the arc of a circle, you can measure the area enclosed by this arc plus two lines that extend from the center of the circle (two radii). This arc-related area is known as a sector. You might have to perform this type of calculation in a high school or college geometry class or in various career fields such as landscaping or engineering.
Notice the angle formed by the two radii. Divide this angle by 360 to find out what portion of the circle it represents. For instance, if the angle is 45 degrees, divide 45 by 360 to get 0.125.
Find the area of the circle by squaring the radius and multiplying that by 3.14 (pi). For example, if the radius is 10 cm, square 10 to get 100. Then multiply 100 times 3.14 to get a circle area of 314 square cm.
Multiply your answer from Step 1 by your answer from Step 2 to find the area of the arc's sector. Therefore, 0.125 times 314 equals 39.25. The area of the arc's sector is 39.25 square cm.