Question

Find the area of the figure. Round to the nearest tenth if necessary. Use 3.14 for . 47.3 units2 41.1 units2 57.1 units2 66.2 units2

Answer 1

41.1 units²

Explanation:

The given figure is composed of a semicircle and a triangle.

The diameter of the circle = the base of the triangle = the distance between point D and point F on the x-axis.

Therefore,

Diameter (d) of circle = 8 units

Radius of circle =
`(diameter)/(2) = (8)/(2)`

`radius (r) = 2`

Base of triangle = 8 units

The height of the triangle = the perpendicular distance between point E and segment DF on the y-axis

Height of triangle = 4 units

=>Area of the figure = area of triangle + area of semicircle

Area of figure =
`(1)/(2)bh + (1)/(2)*pie*r^2`

`= (1)/(2)*8*4 + (1)/(2)*3.14*4^2`

`= (1)/(2)*32 + (1)/(2)*50.24`

`= 16 + 25.12`

`= 41.12`

Area of the figure = 41.1 units² (to the nearest tenth)