Question

A room is shaped like a trapezoid as shown. 23 ft 28 ft 35 ft (a) What is the area of the room? Use the formula A = 2(b + b). Show your work A = = 6 + b. (b) Carpet costs $8.30 per square foot. How much will it cost to carpet the room? Show your work. (c) Furniture covers 25% of the floor. How many square feet of carpet are covered by furniture? Show your work.

Answer 1

a)

The area of a trapezoid is given by:

`A=(1)/(2)h(b_1+b_2)`

In this case the height of the trapezoid is 28 ft and its bases are 23 ft and 35 ft long; plugging this values we have:

`\begin{gathered} A=(1)/(2)(28)(23+35) \\ A=812 \end{gathered}`

Therefore, the area of the room is 812 square ft.

b)

To determine how much it will cost to carpet the room we multiplied the cost per square ft by the total area, then we have:

`8.30(812)=6739.6`

Threfore, it will cost $6,739.60 to carpet the room.

c)

To determine how many square ft of carpet is covered by the furniture we multiply the area of the room by the decimal form of the percentage:

`812(0.25)=203`

Therefore, 203 square ft is covered by the furniture.