Answer:
[tex]\large\boxed{A=(120+32\pi)cm^2}[/tex]
Step-by-step explanation:
Look at the picture.
We have the half of circle and a triangle.
The fromula of an area of a circle:
[tex]A_O=\pi r^2[/tex]
r - radius
We have r = 8cm. Substitute:
[tex]A_O=\pi(8)^2=64\pi\ cm^2[/tex]
The formula of an area of a triangle:
[tex]A_\triangle=\dfrac{bh}{2}[/tex]
b- base
h - height
We have b = 8cm + 8cm = 16cm and h = 15cm. Substitute:
[tex]A_\triangle=\dfrac{(16)(15)}{2}=(8)(15)=120\ cm^2[/tex]
The area of the figure:
[tex]A=\dfrac{1}{2}A_O+A_\triangle[/tex]
Substitute:
[tex]A=\dfrac{1}{2}(64\pi)+120=32\pi+120=(120+32\pi)cm^2[/tex]
