Question

The curved part of this figures is a semicircle.

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

28+16.25π units²

28+8.125π units²

14+16.25π units²

14+8.125π units²

Answer 1

The answer is 14+8.125π units².

Answer 2

`(14+8.125 \pi)\ units^(2)`

Explanation:

we know that

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

Step 1

Find the area of triangle

The area of triangle is

`A=bh/2`

we have

`b=(3-(-4))=7\ units`

`h=(2-(-2))=4\ units`

substitute

`A=(7*4)/2=14\ units^(2)`

Step 2

The area of semicircle is equal to

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

Find the radius

The radius is the half distance between points
`(-4,-2)` and
`(3,2)`

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{(2+2)^(2)+(3+4)^(2)}`

`d=\sqrt{(4)^(2)+(7)^(2)}`

`d=√(65)\ units` -------> is the diameter

the radius is equal to

`r=((1)/(2))√(65)\ units`

Find the area of semicircle

`A=(1)/(2) \pi (((1)/(2))√(65))^(2)`

`A=(65)/(8) \pi\ units^(2)`

`A=8.125 \pi\ units^(2)`

Step 3

Find the area pf the figure

`14\ units^(2)+8.125 \pi\ units^(2)`

`(14+8.125 \pi)\ units^(2)`