Question

You have just bought a new home, and the builder has shown you the blueprints for one of the rooms in the house. It is a rectangular room with a semi circular wall which is pictured below but it is not drawn to scale. For all calculations involving pi, use 3.14Dimensions 11ft by 14ft A) you are going to put crown molding around the top edge of each one add flair to the transition between the wall and the ceiling. How much crown molding would you need to purchase for this room? Amount of crown molding needed= _____ feet.B) How much flooring would need to be purchased for the room?Amount of flooring needed= ____ square feet.

Answer 1

Part A.

In this case, we need to find the perimeter of the figure, which is equal to the lenght of the three side and the semicircle.

Since the arc of the semicircle has a lenght of one half the circunference,

`\text{ arc lenght=}\frac{2\pi r\text{ }}{2}=\pi r`

where, in our case, the radius is

`r=(11)/(2)=5.5`

then, the arc lenght of the semicircle is3

`\text{arc lenght=3.1416}*5.5=17.28\text{ ft}`

Therefore, the Perimeter of the figure is

`\begin{gathered} \text{Perimeter}=14+11+14+17.28 \\ \text{Perimeter}=56.28\text{ ft} \end{gathered}`

Therefore, the answer for part A is 56.28 feet.

Part B.

In this case, we need the area of the semicircle and the area of the rectangle below it, that is,

The area of the semicircle is half the area of the circle, that is,

`\begin{gathered} \text{area semicircle=}(\pi r^2)/(2)=((3.1416)(5.5^2))/(2) \\ \text{area semicircle=}47.5167ft^2 \end{gathered}`

and the area of the rectangle is

`\text{area rectangle=11}*14=154ft^2`

Therefore, the total area is

`47.5167+154=204.5167ft^2`

Therefore, the answer for part B is: 204.52 square feet