Question

Sandy needs to add trim to the carpet she has added in her game room. How many feet of wood trim will she need to complete her project if the diameter of the semicircle portion of her room is 12 ft? Wood trim is only sold in whole number quantities. Do not include units in your answer.

Answer 1

Given:

diameter of semi-circle = 12 ft

The number of feet needed to complete the project is the perimeter of the carpet as shown in the diagram.

We need to find the circumference of the semi-circle and then sum up the lengths.

The perimeter of a semi-circle can be found using the formula:

`=\text{ }\pi\text{r + d}`

where r is the radius of the semi-circle and

d is the diameter of the semi-circle.

The perimeter of the semicircle is:

`\begin{gathered} =\text{ }\pi\text{ }*(12)/(2)\text{ + 12} \\ \text{= 30.85 ft} \end{gathered}`

The total perimeter would be:

`\begin{gathered} =\text{ 6 + 7.8 + 30.85} \\ \text{= 44.65} \\ \approx\text{ 45} \end{gathered}`

Hence, Sandy would need 45 ft of wood trim for the project.

Answer:

45