SEARCH HOME
Math CentralQuandaries & Queries

search

Question from Connie, a parent:

How do you find surface area if the rectangle is 100ft. by 200ft. with quarter circles in the corners with a radius of 20ft?

Hi Connie,

Start with a rectangle 100 feet by 200 feet which has area 100 × 200 square feet. From each corner remove a square which is 20 feet by 20 feet.

rectangle

The area remaining is

100 × 200 - 4 × 20 × 20 = 20000 - 4 × 202 = 20000 - 1600 = 18400 square feet.

Take a circle of radius 20 feet, cut it into four quarter circles and place the quarter circles in the missing corners of the rectangle.

rounded rectangle

The area of a circle of radius 20 feet is π × 202 square feet so the area of the rectangle with rounded corners is

18400 + π × 202 = 18400 + 1256.6 = 19656.6 square feet.

Penny

About Math Central
 

 


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS