Question

can you help me out with a question

Answer 1

The shape consists of half a circle on top of a trapezium.

The dimensions of the trapezium are given:

Base 1 = 9 m

Base 2 = 23 m

Height = 7 m

The radius of the circle is half the diameter:

r = 9/2 = 4.5 m

Now compute the area of the trapezium:

$A_t=\frac{b1+b2}{2}\cdot h$

Substituting:

$A_t=\frac{9m+23m}{2}\cdot7m=\frac{32m}{2}\cdot7m=16\cdot7m^2=112m^2$

The area of the semicircle is:

$A=\frac{\pi r^2}{2}$

Substituting:

$A_c=\frac{\pi4.5^2}{2}$

Calculating:

Ac=31.8 square m

The total area of the shaded figure is:

At = 112 + 31.8 = 143.8 square m