Question

The square below has side 10x. Find the area of the square remaining after a circle of radius 2x is removed from the square; in other words, find the area of the shaded region in factored form.

Answer 1

Area of a square: side^2
Area of a circle: (pi)(radius^2)
A(square)=(10x)^2
A(circle)=(pi)(2x)^2
A(square)=100x^2
A(circle)=(pi)4x^2
Shaded Area=A(square)-A(circle)
Shaded Area=100x^2-(pi)4x^2
=4x^2(25-(pi))