Question

What is the approximate area of the shaded portion of the diagram? (Use 3.14 as an estimate for pi.)

Answer 1

218

Explanation:

first find the area of the circle-

`A=\pi r^(2) \\A=\pi 10^(2) \\A=100\pi \\A=314`

to find the area of the triangle, we need the base and the height. The base we know is 16, since we don't know the height yet, use the Pythagorean theorem to find the height. One leg is 16 the hypotenuse is 20 (2* the radius).

`a^(2) +b^(2) =c^(2) \\a^(2) +16^(2) =20^(2) \\a^(2) +256=400\\a^(2) =144\\a=12`

Now I know the height is 12. Find the area of the triangle

`A=(1)/(2) bh\\A=(1)/(2) (16)(20)\\A=96`

subtract the area of the triangle from the area of the circle

314-96=218