Circular Garden

Ebru’s backyard is a square with side length of 20 meters. Her backyard has a circular garden that extends to each side of the yard. In the center of the garden is a square patch of asparagus so big that each corner of the square touches a side of the garden. How much area in Ebru’s garden is not being used to grow asparagus?
Source: NCTM Mathematics Teacher, January 2006

SOLUTION
image
Area of circle
\pi 10^2=100\pi
Triangle ABC is a 45^\circ\!\textrm{-}45^\circ\!\textrm{-}90^\circ triangle
BC=10\sqrt 2
Area of inner square
(10\sqrt 2)^2=200
Area of garden not used to grow asparagus
100\pi\!-\!200 squared meters

Answer: 100\pi\!-\!200 squared meters

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About mvtrinh

Retired high school math teacher.
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