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ABCD is a right trapezium with AB parallel to CD and ∠BAD=∠ADC=90∘. The diagonals AC and BD intersect at E. If AB=7, DC = 28 and AD = 75AD=75, what is the area of triangle BEC?

 Jun 29, 2020
 #1
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ABCD is a right trapezium with AB parallel to CD and ∠BAD=∠ADC=90∘. The diagonals AC and BD intersect at E. If AB=7, DC = 28, and  AD = 75, what is the area of triangle BEC?

 

Area of a triangle BEC = 210 units squared.  smiley

 Jun 29, 2020
 #2
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1)  Calculate angles   DAC  and  DBM     ( ∠DAC = ∠MNC = ∠ENB )    ( ∠DBM = ∠EBN )

 

2)  Find line segments     MN  and  BN

 

3)  Find the area of a triangle  BNC

 

4)  Find the area of a triangle  BEN  using the law of sines and Heron's formula.

 

Add these two areas ( BNC and BEN ) and you're done.  smiley

 

( Btw, the above post is mine toolaugh)

 

Dragan  Jun 29, 2020
edited by Dragan  Jun 29, 2020

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