The curved part of this figure is a semicircle. what is the best approximation for the area of this figure?
(a). 21+7.25π units²
(b). 21+14.5π units²
(c). 10.5+7.25π units²
(d). 10.5+14.5π units²

The answer is the option

Step-by-step explanation:

we know that

the area of the figure is equal to the area of semicircle plus the area of a triangle

Find the area of semicircle

we know that

The area of semicircle is equal to

Let

The distance AB is equal to the diameter of semicircle

the formula to calculate the distance between two points is equal to

substitute the values

 -----> diameter of the semicircle

so the radius is equal to

find the area of semicircle

Find the area of the triangle

we have

Observing the figure

substitute

Find the area of the figure

substitute

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,