A square is inscribed in a circle of radius 1 unit, and a larger square is circumscribed about the same circle. What is the area of the region located between the two squares?

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2 Answers
CW
Jan 11, 2018

#A=2 " unit"^2#

Explanation:

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Area of a square is given by : #A=1/2d^2#, where #d# is the length of the diagonal of the square.
Given radius of the circle #r=1#,
#=> OA=1#,
#=> "diagonal of the smaller square"=AB=2*OA=2#,
#=> "area of the smaller square " A_S=1/2*AB^2=1/2*2^2=2#
#=> OE="radius"=1, => ED=1#,
#=> CD=2ED=2#
#=> "area of the larger square " A_L= CD^2=2^2=4#
Hence, area of the region located between the two squares #=# shaded area #= A_L-A_S=4-2=2 " unit"^2#

sankarankalyanam
Jan 11, 2018

Difference in areas of the two squares = 2 sq. units

Explanation:

radius of circle #r = 1#

Diagonal of inner square # d_s = 2r = 2#

Area of inner square #A_s = (1/2) (d_s)^2 = (1/2) * 2^2 = 2#

Side of outer square #a_S = 2r = 2#

Area of outer square #A_S = a^2 = 2^2 = 4#

Difference in areas = 4 - 2 = 2 sq. units

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