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}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%283%2B4%29%5E2%2B%282%2B2%29%5E2%7D)
![=\sqrt{7^2+4^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B7%5E2%2B4%5E2%7D)
![=\sqrt{49+16}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B49%2B16%7D)
unit,
Thus, the radius of the semicircle = √65/2 unit,
⇒
![= \frac{1}{2}\pi(\frac{65}{4})](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1%7D%7B2%7D%5Cpi%28%5Cfrac%7B65%7D%7B4%7D%29)
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)]](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B2%7D%5B-4%282-2%29%2B3%282%2B2%29-4%28-2-2%29%5D)
![=\frac{1}{2}\times 28](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%2028)
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)
square unit.
⇒ Fourth option is correct.