If the perimeter and radius of a sector are 38 and 9 cm respectively . find its area.
+128474 The perimeter is given by :
2* radius + arc lengrh of the sector =
2r + r* theta where theta is the measure of the central angle of the sector ( in radians)
So we have that
38 = 2r + r * theta simplify
38 = r ( 2 + theta) subbing in for the radius we have that
38 = 9 (2 + theta) divide both sides by 9
(38/9) = 2 + theta subtract 2 from both sides
20/9 = theta
The area of the sector = (1/2)* r^2 * theta
So....the area = (1/2) (9)^2 * ( 20/9) = (1/2) ( 9) (20) = 90 cm^2
