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Two \(2 \times 3\) rectangles are drawn, as shown. Find the area of their overlap, which is shaded.

 May 8, 2020
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Let the crosspoint of the diagonals of the rhombus be an N.

 

Let the crosspoint of AD and BF be an M

 

BN = [sqrt(2² + 3²)] / 2 = 1.802775638

 

tan(∠FBD) = 2 / 3             ∠FBD = 33.69006753°

 

NM = BN * tan(∠FBD)   =   1.201850425

 

Shaded area       A= ( BN * NM ) * 2  =  4.3333333333 units squared  indecision

 May 8, 2020
edited by Guest  May 8, 2020

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