# A circular rug has a radius of (4x-6). What is the area of the rug?

Jan 28, 2017

$A = 16 \pi {x}^{2} - 48 \pi x + 36 \pi$

#### Explanation:

Remember the area of a circle's formula is
$A = \pi {r}^{2}$

In this case $r = \left(4 x - 6\right) \implies {r}^{2} = {\left(4 x - 6\right)}^{2} = \left(4 x - 6\right) \left(4 x - 6\right)$

Then using FOIL we get

${r}^{2} = {\left(4 x - 6\right)}^{2} = 16 {x}^{2} - 48 x + 36$

Then the area of the rug $A$ is

$A = \pi {r}^{2} = 16 \pi {x}^{2} - 48 \pi x + 36 \pi$