Question

The curved part of this figure is a semicircle.

Answer 1

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.

$d = \sqrt{3^2 + 8^2}$

$d \approx 8.544$

The radius is half the diameter.

$r = \dfrac{d}{2} = \dfrac{8.544}{2} = 4.272$

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

$A = \dfrac{bh}{2} + \dfrac{\pi r^2}{2}$

$A = \dfrac{3 \times 8}{2} + \dfrac{\pi \times 4.272^2}{2}$

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