Question

Can you please help me answer my homework question and give me an explanation so I can follow along

Answer 1

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:

`A_(semicircle)=(\pi r^2)/(2)`

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.

`A_(semi-circle)=((3.14)(3cm)^2)/(2)`

Then, solve.

`A_(semi-circle)=(3.14(9cm^2))/(2)`
`A_(semi-circle)=(28.26cm^2)/(2)`
`A_(semi-circle)=14.13cm^2\frac{}{}`

The area of the semi-circle is 14.13 cm².

Let's now calculate the area of the triangle. The formula is:

`A_(triangle)=(base* height)/(2)`

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.

`A_(triangle)=(6cm*3cm)/(2)`

And solve.

`A_(triangle)=(18cm^2)/(2)=9cm^2`

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.

`14.13cm^2-9cm^2=5.13cm^2`

Therefore, the area of the shaded region is 5.13 cm².