Question

2022 - q9
9 chad will have new carpet put on the rectangular floors of two rooms in his house. one floor is 12 1/2 feet long, and the other floor is 15 3/4 feet long. each floor has a width of 10 feet. what is the total area in square feet of the new carpet?

Explanation:

Step1: Convert mixed - numbers to improper fractions

$15\frac{3}{4}=\frac{15\times4 + 3}{4}=\frac{63}{4}$ and $12\frac{1}{2}=\frac{12\times2+1}{2}=\frac{25}{2}$

Step2: Calculate the area of the first floor

The area of a rectangle is $A = l\times w$. For the first floor with length $l_1=\frac{63}{4}$ feet and width $w = 10$ feet, the area $A_1=\frac{63}{4}\times10=\frac{63\times10}{4}=\frac{630}{4}=\frac{315}{2}$ square feet.

Step3: Calculate the area of the second floor

For the second floor with length $l_2=\frac{25}{2}$ feet and width $w = 10$ feet, the area $A_2=\frac{25}{2}\times10=\frac{25\times10}{2}=125$ square feet.

Step4: Calculate the total area

The total area $A = A_1+A_2=\frac{315}{2}+125$. We rewrite $125$ as $\frac{250}{2}$. Then $A=\frac{315 + 250}{2}=\frac{565}{2}=282.5$ square feet.

Answer:

$282.5$ square feet