Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of pi (no approximations.) This one is a bit different than the other ones I have searched.

The area of the shaded portion is: 36πcm² – 72cm² = 36(π – 2)cm²

Step-by-step explanation:

The diagram referred to has been attached.

The given shape is the quarter of a circle. To find the area of the shaded portion, we need to know the area of the whole quarter circle and then know the area of the triangle. If we do this, we can then subtract the area of the triangle from the quarter circle so that it remains just the shaded part.

The area of a quarter circle is given as (1/4)πr² where r is the radius.

The radius of the quarter circle is 12cm. Therefore, the area of the quarter circle is:

(1/4) x π x (12)² = (1/4) x π x 12 x 12 = π x 3 x 12 = 36πcm².

The area of the triangle is given as (1/2)bh where b is the base and h is the height.

The base is the same as the height since radius of a circle (and a quarter circle is a circle divided into 4 quadrants) is the same all through.

Therefore, b = h = 12. Hence, the area of the triangle is:

(1/2) x 12 x 12 = 6 x 12 = 72cm²

The area of the shaded portion is now: 36πcm² – 72cm² = 36(π – 2)cm²

circle area = pi * radius^2

if diameter = 10 then radius = 5

circle area = pi * 5^2

circle area = pi * 25

circle area = 78.5398163397 square units

step-by-step explanation: