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Two rectangles overlap, as shown below. Find the area of the overlapping region (which is shaded) if AB = BE = 2 and AD = ED = 4.

 

 

 Nov 21, 2022
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Let the height of the bottom triangle with the base DC==x
Hypotenuse^2 - x^2 ==2^2
[4 - x]^2 - x^2==4, solve for x
x ==1.5
Area of the bottom triangle ==[2 x 1.5] / 2==1.5 u^2
Since you have 2 similar triangles (bottom + top), therefore their combined area ==2 x 1.5 ==3 u^2
Area of vertical rectangle ==2 x 4 ==8 u^2
Therefore, area of the shaded part==8 - 3 == 5 u^2

 Nov 21, 2022

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