You are given a circle of radius 12. What is the segment area of an arc that is 90 degrees?

144π - 72 sq in.
36π - 72 sq in.
36π - 144 sq in.

36π - 72 sq in.

Step-by-step explanation:

π×12² = 144π

90/360 × 144π = 36π

Triangle = ½ × 12 × 12 = 72

Segment = 36π - 72

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: