Question

The circle on the right has center O. Its radius is 3 yd., and the central angle a measures 130°. What is the area of the shaded region? Give the exact answer in terms of π, and be sure to include the correct unit in your answer.

Answer 1

area of the sector = 3.25π yard²

Explanation:

The radius of the circle is 3 yards . The central angle is 130° let us say it is the sector angle of the circle. The angle is 130°. If the shaded area of the circle is the sector area of the circle the area of the sector can be computed below.

area of a sector = ∅/360 × πr²

where

∅ = center angle

r = radius

area of the sector = 130/360 × π × 9

area of the sector = 1170π/360

area of the sector = 3.25π yard²

If the shaded area is segment. The shaded area can be solved with the formula.

Area of segment = area of sector - area of the triangle

Area of segment = ∅/360 × πr² - 1/2 sin∅ r²

The picture demonstrate the area of sector and the segment of a circle with illustration on how to compute the area of the triangle