The boundary of a park is shaped like a circle. The park has a rectangular playground in the center and 2 square flower beds, one on each side of the playground. The length of the playground is l and its width is w. The length of each side of the flower beds is a. Which two equivalent expressions represent the total fencing material required to surround the playground and flower beds? Assume that the playground and beds do not overlap.

Answer 1

The circumference of the circle is 2πr, where r is the radius of the circle. Since the park is shaped like a circle, the circumference represents the total fencing material required to surround the park.
The radius of the circle is equal to half the length of the playground, or l/2.
So, the total fencing material required to surround the park is 2π(l/2) = πl.
Alternatively, the total fencing material required to surround the park is also equal to the sum of the perimeters of the rectangular playground and the two square flower beds.
The perimeter of the rectangular playground is equal to 2(l + w).
Since there are two square flower beds, each with a side length of a, the total perimeter of the flower beds is equal to 4a.
So, the total fencing material required to surround the park is 2(l + w) + 4a.