Shaded Regions!

Geometry Level 1

AEBF and ABCD both are square. If AE=2, then what is the Area of the Shaded Region(black)?

4 None 2 6

Mamun Abdullah by Mamun Abdullah , 32, Bangladesh

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2 solutions

By Pythagorean theorem: A B = 2 2 + 2 2 = 4 ( 2 ) = 2 2 AB=\sqrt{2^2+2^2}=\sqrt{4(2)}=2\sqrt{2} .

The area of the shaded region is equal to the area of square A B C D ABCD minus the area of triangle A B F ABF .

A = ( 2 2 ) 2 − 1 2 ( 2 ) ( 2 ) = 8 − 2 = 6 A=(2\sqrt{2})^2-\dfrac{1}{2}(2)(2)=8-2=\boxed{6}

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Bec Freeman
Sep 5, 2015

We know that AE=2 so then AB=((2^2)+(2^2))^(1/2)=8^(1/2) then the area of ABCD is 8^(1/2)+8^(1/2)=8 and the area of the triangle ABF=(1/2) 8^(1/2) (1/2) 8^(1/2) =2 8-2=6 Tadaa!

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