Question

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

Answer 1

Answer:10.5+7.25 pie

Explanation:

for the points

Answer 2

The answer is the option

`(10.5+7.25\pi)\ units^(2)`

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

`A1=(1)/(2)\pi r^(2)`

Let

`A(-5,-2), B(2,1)`

The distance AB is equal to the diameter of semicircle

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

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

substitute the values

`d=\sqrt{(1+2)^(2)+(2+5)^(2)}`

`d=\sqrt{(3)^(2)+(7)^(2)}`

`dAB=√(58)\ units` -----> diameter of the semicircle

so the radius is equal to

`r=0.5√(58)\ units`

find the area of semicircle

`A1=(1)/(2)\pi (0.5√(58))^(2)`

`A1=(1)/(8)\pi (58)`

`A1=7.25\pi\ units^(2)`

Find the area of the triangle

`A2=(1)/(2)bh`

we have

Observing the figure

`b=7\ units`

`3=3\ units`

substitute

`A2=(1)/(2)*7*3=10.5\ units^(2)`

Find the area of the figure

`A=A1+A2`

substitute

`7.25\pi\ units^(2)+10.5\ units^(2)\\ \\(10.5+7.25\pi)\ units^(2)`