Question

2. 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 h1b + b ). Show your work. 2 (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

Given:

$\begin{gathered} \text{ Base }b_1=23\text{ ft, }b_2=35\text{ ft} \\ \text{ Height,}h=28\text{ ft} \end{gathered}$

Required: Area of the room, cost to carpet the room and square feet of carpet are covered by furniture

Explanation:

a) Plug the values into the formula

$A=\frac{1}{2}h(b_1+b_2)$

gives

$\begin{gathered} A=\frac{1}{2}\cdot28\cdot(23+35) \\ =812\text{ ft}^2 \end{gathered}$

Area of the room is 812 square feet.

b) Cost of carpet per square foot = $8.30

Cost to carpet the room

$\begin{gathered} =\text{ Area of the room}\times\text{ Cost of carpet per square foot} \\ =812\times8.30 \\ =6739.6 \end{gathered}$

Cost to carpet the room is 6739.6 dollars.

c) Area of the furniture covers = 25% of Area of the room

$\begin{gathered} =\frac{25}{100}\cdot812 \\ =203 \end{gathered}$

So, 203 square feet of carpet are covered by furniture.

Final Answer: a) Area of the room is 812 square feet.

b) Cost to carpet the room is 6739.6 dollars.

c) 203 square feet of carpet are covered by furniture.