In order to find the area of the shaded region, we need to subtract the area of the triangle from the area of the semi-circle.
First, let's calculate the area of the semi-circle. The formula is:
[tex]A_{semicircle}=\frac{\pi r^2}{2}[/tex]
As mentioned in the question, the radius is 3 cm and the value of π is 3.14. Let's plug them into the formula above.
[tex]A_{semi-circle}=\frac{(3.14)(3cm)^2}{2}[/tex]
Then, solve.
[tex]A_{semi-circle}=\frac{3.14(9cm^2)}{2}[/tex][tex]A_{semi-circle}=\frac{28.26cm^2}{2}[/tex][tex]A_{semi-circle}=14.13cm^2\frac{}{}[/tex]
The area of the semi-circle is 14.13 cm².
Let's now calculate the area of the triangle. The formula is:
[tex]A_{triangle}=\frac{base\times height}{2}[/tex]
As shown in the diagram, the height of the triangle is 3 cm while its base is 6 cm. It is 6cm because the base of the triangle is twice the length of the radius.
Let's plug this into the formula for the area of the triangle.
[tex]A_{triangle}=\frac{6cm\times3cm}{2}[/tex]
And solve.
[tex]A_{triangle}=\frac{18cm^2}{2}=9cm^2[/tex]
The area of the triangle is 9 cm².
Let's now solve for the area of the shaded region by subtracting the area of the triangle from the area of the semi-circle.
[tex]14.13cm^2-9cm^2=5.13cm^2[/tex]
Therefore, the area of the shaded region is 5.13 cm².
