Question

The curved part of this figures is a semicircle.

Answer 1

Answer:

$(14+8.125 \pi)\ units^{2}$

Step-by-step 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

$A=\frac{1}{2} \pi r^{2}$

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

$d=\sqrt{(2+2)^{2}+(3+4)^{2}}$

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

$d=\sqrt{65}\ units$  -------> is the diameter

the radius is equal to

$r=(\frac{1}{2})\sqrt{65}\ units$

Find the area of semicircle

$A=\frac{1}{2} \pi ((\frac{1}{2})\sqrt{65})^{2}$

$A=\frac{65}{8} \pi\ units^{2}$

$A=8.125 \pi\ units^{2}$

Step 3

Find the area pf the figure

$14\ units^{2}+8.125 \pi\ units^{2}$

$(14+8.125 \pi)\ units^{2}$

Answer 2

The answer is 14+8.125π units².