Question

A circular mirror is surrounded by a square metal frame. The radius of the mirror is 5x. The side length of the metal frame is 15x. What is the area of the metal frame? Write your answer in factored form.

Answer 1

Answer:

$-25x^{2} (\pi -9)$

Step-by-step explanation:

The area of the metal frame is equal to the area of the square minus the area of the circle.

The area of the square is the side length squared:

$(15x)^{2}$

$=225x^{2}$

The area of the circle is $\pi r^{2}$, with $r$ being the radius:

$\pi (5x)^{2}$

$=\pi *25x^{2}$

$=25\pi x^{2}$

Now find the area of the metal frame:

$225x^{2} -25\pi x^{2}$

$25x^{2} (9-\pi )$   Factor out the GCF, $25x^{2}$

$-25x^{2} (\pi -9)$   Factor out a $-1$