Question

Find the area of a compound shape Can you please explain

Answer 1

Answer:

$A=292.53~m^2$

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:

$A_c = \pi r^2$

The area of a triangle of base b and height h is:

$\displaystyle A_t=\frac{b.h}{2}$

Calculate the area of the circle:

$A_c = \pi 8^2$

$A_c = 64\pi$

Area of half the circle:

$A_c/2 = 32\pi~m^2$

Area of the triangle:

$\displaystyle A_t=\frac{24\cdot 16}{2}$

$A_t=192~m^2$

The area of the shaded shape is:

$A=32\pi~m^2+192~m^2$

Substituting the value of pi:

$\mathbf{A=292.53~m^2}$