Question

The circular rug is placed on a square floor that is 14ft. The rug touches all four walls. How much of the floor space is not covered by the rug?

Answer 1

check the picture below.

so, the area of the square is really 14x14, and that includes the rug.

now, if we could just get the area of the circular rug, and "subtract" it from the square's, in effect making a hole in the square, what's leftover is what's not covered by the rug.


`\bf \textit{area of a circle}\\\\ A=\pi r^2\quad \begin{cases} r=radius\\ -----\\ r=7 \end{cases}\implies A=\pi 7^2\implies A=49\pi \\\\ -------------------------------\\\\ \stackrel{square's~area}{14\cdot 14}~~~-~~~\stackrel{rug's~area}{49\pi }\implies \stackrel{uncovered~area}{196-49\pi }`