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

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Answer 1 · 2017-01-28T02:40:37

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

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

In this case $r = (4 x - 6) \Rightarrow r^{2} = {(4 x - 6)}^{2} = (4 x - 6) (4 x - 6)$ $r=(4x-6) => r^2=(4x-6)^2=(4x-6)(4x-6)$

Then using FOIL we get

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

Then the area of the rug $A$ $A$ is

$A = π r^{2} = 16 π x^{2} - 48 π x + 36 π$ $A=pir^2=16pix^2-48pix+36pi$

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