Question

The curved part of this figures is a semicircle.

Answer 1

The answer is 14+8.125π units².

Answer 2

Answer: 14+8.125π units²

Step-by-step explanation:

By the given diagram,

The diameter of the semicircle = The line segment having the end points (-4,-2) and (3,2),

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

$=\sqrt{7^2+4^2}$

$=\sqrt{49+16}$

$=\sqrt{65}$  unit,

Thus, the radius of the semicircle = √65/2 unit,

⇒ $\text{Area of the semicircle}=\frac{1}{2}\pi(\frac{\sqrt{65}}{2})^2$    

$= \frac{1}{2}\pi(\frac{65}{4})$

$=\frac{65\pi}{8}$ square unit.

Now, by the given diagram,

The area of the triangle having the vertices (-4,-2), (3,2) and (-4,2)  ( By the coordinate form of area of a triangle formula )

$=\frac{1}{2}[-4(2-2)+3(2+2)-4(-2-2)]$

$=\frac{1}{2}\times 28$

$=14$ square unit,

Hence, the total area of the given figure = Area of semicircle having diameter √65 + area of triangle having vertices (-4,-2), (3,2) and (-4,2)

$=\frac{65\pi}{8}+14$

$=(8.125\pi+14)$ square unit.

⇒ Fourth option is correct.