Question

Use the composite figure below to answer questions 4 and 5.

Four congruent circles create rounded corners on a rectangular carpet. A quarter of the circle overlaps each corner.




Find the area and perimeter  of the figure to the nearest tenth.

A.
321,212.1 inches2

B.
303,053.5 inches2

C.
322,107.5 inches2

D.
302,912.1 inches2

Answer 1

895 inches + 1 diameters = 915 inches
1 diameter = 915 -895 = 20 inches (radius = 10 inches)

The rectangle Diagonal = 1,000 -20 = 980 inches

(Left Side of the rectangle)^2 = 980^2 - 915^2
(Left Side of the rectangle)^2 = 960,400 -837,225
(Left Side of the rectangle)^2 = 123,175 inches

Rectangle Left Side = 350.9629610087 inches

Rectangle Area = 915 * 350.9629610087 = 321,131.11 square inches

Area of THREE circles = 3 * PI * 10^2

Area of THREE circles = 942.48 square inches

TOTAL AREA = 321,131.11 + 942.48 = 322,073.59 square inches

That's about as well as I could do.