Question

An ice rink is 200 feet long and 85 feet wide. The four corners of the rink are rounded to a radius of 24 feet. What is the surface area of the rink? Round the answer to the nearest square foot.

Answer 1

Answer:

16,506 ft²

Explanation:

There are different ways you can divide the area using rectangles and circles.  One way is to find the area of the entire width and length, then subtract the empty areas in the corners.

If we take the empty areas and put them together, we find their area is the area of a square minus the area of a circle.

A = (2r)² − πr²

A = 4r² − πr²

A = (4 − π) r²

So the area of the rink is:

A = WL − (4 − π) r²

A = (85)(200) − (4 − π) (24)²

A ≈ 16,506 ft²