Question

The curved part of this figure is a semicircle.

What is the best approximation for the area of this figure?


24+18.25π units²

12+9.125π units²

12+18.25π units²

24+9.125π units²

Answer 1

The answer is 12+9.125π units²

Attached is a picture of the answer on the test.

Hope this helps :) !

Answer 2

Draw the diameter from point (-1, -5) to point (2, 3).

The triangle has base 3 and height 8.

The diameter of the semicircle is the hypotenuse of the triangle.


`d = √(3^2 + 8^2)`


`d \approx 8.544`

The radius is half the diameter.


`r = (d)/(2) = (8.544)/(2) = 4.272`

The total area is the area of the triangle plus the area of the semicircle.


`A = (bh)/(2) + (\pi r^2)/(2)`


`A = (3 * 8)/(2) + (\pi * 4.272^2)/(2)`


`A = 12 + 9.125 \pi`
`units^2`