Question

In the diagram shown at the right, a 2-foot-wide flower border surrounds the heart-shaped pond. What is the area of the border?

Answer 1

The area is 139.02 sq. ft.

This can be broken into two shapes:  a 12 by 12 square and a circle with a diameter of 12.  Adding the 2 ft border increases it to a 14 by 14 square and a circle with a radius of 16 (2 on each side).  

With border:

Area of square = 14*14 = 196
Area of circle = 3.14(8*8) = 200.96

Together = 396.96

Without border:

Area of square = 12*12 = 144
Area of circle = 3.14(6*6) = 113.04

Together = 257.04

This is a difference of 396.96-257.04 = 139.02 sq. ft.