Mrs. Isabelle is making paper and plastic foam animals for her first-grade class. She is calculating the amount of wasted materials for environmental and financial reasons. Mrs. Isabelle is cutting circles out of square pieces of paper to make paper animals in her class. Enter the polynomial that represents the amount of paper wasted if the class cuts out the biggest circles possible in squares of length l. The polynomial that represents the amount of paper wasted is

Since the length of the square is l, the area would be l*l = l².

The area of the circle is given by the formula A=πr². In this case our radius, r, is 1/2 the length of the square, or 1/2l. This makes the area of the circle A=π (1/2l) ²=π (1/4l²) = π (1/4) (l²) = 1/4πl². (Remember, multiplication is commutative, which means we can switch these around to make them easier for us.)

The wasted area would be the area of the square minus the used area of the circle, or

l²-1/4πl²