Question

P. The Shah family basement floor is shaped like a trapezoid. The basement has sides of and 24 feet and two sides of 21 feet. They are going to carpet the basement. The carpeting will cost $35 per square yard. A. What is the area, in square feet, of the basement foor? Show your work. B. What is the cost to carpet the basement floor? Explain how you found your answer

Answer 1

A.

In order to calculate the area of the trapezoid, we need to calculate its height:

Using the Pythagorean Theorem, we have:

`\begin{gathered} 21^2=h^2+6^2 \\ 441=h^2+36 \\ h^2=441-36 \\ h^2=405 \\ h=20.12 \end{gathered}`

Now, calculating the area:

`\begin{gathered} A=((B+b)h)/(2) \\ A=((36+24)20.12)/(2) \\ A=60\cdot10.06 \\ A=603.6 \end{gathered}`

B.

If each square yard is $35, first let's convert the area from ft² to yd² (1 yard = 3 feet, 1 yd² = 9 ft²):

`A=603.6\text{ ft}^2=(603.6)/(9)\text{ yd}^2=67.07`

So the total cost is:

`\text{cost}=67.07\cdot35=2347.45`

So the cost is approximately $2347.45.