Answer:
[tex]A=292.53~m^2[/tex]
Step-by-step explanation:
Area of a Compound Shape
The shape shown in the image is made of two shapes: Half a circle of radius 8 m and a triangle of base 24 m and height 16 m.
The area of a circle of radius r is:
[tex]A_c = \pi r^2[/tex]
The area of a triangle of base b and height h is:
[tex]\displaystyle A_t=\frac{b.h}{2}[/tex]
Calculate the area of the circle:
[tex]A_c = \pi 8^2[/tex]
[tex]A_c = 64\pi[/tex]
Area of half the circle:
[tex]A_c/2 = 32\pi~m^2[/tex]
Area of the triangle:
[tex]\displaystyle A_t=\frac{24\cdot 16}{2}[/tex]
[tex]A_t=192~m^2[/tex]
The area of the shaded shape is:
[tex]A=32\pi~m^2+192~m^2[/tex]
Substituting the value of pi:
[tex]\mathbf{A=292.53~m^2}[/tex]
