A cow is tethered by a 120ft rope to the inside corner of an

A cow is tethered by a 120-ft rope to the inside corner of an L-shaped building, as shown in the figure. Find the area that the cow can graze. (Let a = 10 ft, b = 60 ft, c = 120 ft, d = 70 ft, and e = 60 ft. Round your answer to the nearest whole number.) ft^2

Solution

you have 4 quadrants

area of a circle = pi*r^2
the area of each quadrant is( 1/4)*pi*r^2

1 quadrant is radius 120
1 quadrant is radius (120 - 70) =50
1 quadrant is radius (120 - 60 ) =60
1 quadrant is radius (120 - 60 - 10) =50

the total area is the sum of these 4 areas

(1/4)*pi*120*120 = 11,304.
(1/4)*pi*50 * 50 = 1,962.5.
(1/4)*pi*60 * 60 = 2,826.
(1/4)*pi*50 * 50 = 1,962.5

total = 11,304+1,962.5+2,826+1,962.5

= 180,55. (square feet)