Answer:
The area of the shaded region is: 32.25m^2
Step-by-step explanation:
Given
See attachment for rectangle and semicircles
Required
The shaded region
We have:
[tex]l =30[/tex] --- length of the rectangle
This means that the diameters of the three circles add up to 30m.
So, the diameter of 1 is:
[tex]d = l/3[/tex]
[tex]d = 30/3[/tex]
[tex]d = 10[/tex]
The area of one circle is:
[tex]A_1 = \pi * \frac{d^2}{8}[/tex]
[tex]A_1 = 3.14 * \frac{10^2}{8}[/tex]
[tex]A_1 = 3.14 * \frac{100}{8}[/tex]
[tex]A_1 = 39.25m^2[/tex]
The area of the three circles is:
[tex]A_2 = 3 * A_1[/tex]
[tex]A_2 = 3 *39.25m^2[/tex]
[tex]A_2 = 117.75m^2[/tex]
The area of the rectangle is:
[tex]A_3 = 30 * r[/tex]
Where r is the radius of the circle
And
[tex]r =d/2[/tex]
[tex]r =10/2[/tex]
[tex]r =5[/tex]
So, we have:
[tex]A_3 = 30 * r[/tex]
[tex]A_3 = 30 * 5[/tex]
[tex]A_3 = 150[/tex]
So, the shaded region is:
[tex]A_4 = A_3 - A_2[/tex]
[tex]A_4 = 150 - 117.75[/tex]
[tex]A_4 = 32.25m^2[/tex]
