Question

There is a circular garden in the middle of a square yard. The radius of the circle is 4x. The side length of the yard is 20x. What is the area of the part of the yard that is not covered by the circle?

Answer 1

We have a circle inside of a square, so the area of the yard that is NOT covered by the garden will be:

Area of square - Area of circle

The area of a square is the side length squared, or s^2.
The area of a circle is pi * (radius squared), or pi * r^2.

This means we are looking for:

s^2 - pi*r^2

We are given s = 20x, and r = 4x, so we plug these in:

(20x)^2 - pi * (4x)^2

Expand:

400x^2 - pi * (16x^2)

This can be factored to get:

16x^2 * (25 - pi) square units not covered by garden.

Answer 2

I got to the 400x^2 -pi *(16x^2). After that I am lost as to how you factor this!