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Trapezoid ABCD has base 20 units and base 40 units. Diagonals AC and BD intersect at X. If the area of trapezoid ABCD is 900 square units, what is the area of triangle BXC?

 Jul 4, 2022
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Find the height of the trapezoid

 

900 =  (h/2)  ( 20 + 40)

 

900 / 60  =  h /2

 

15 = h /2

 

h  = 30

 

Triangles   AXB     and  CXD   are similar

 

Call AB the shorter base and CD the longer

 

Since the base of triangle    CXD  is twice that of  triangle AXD.....their scale factor  is 2/1

 

So....the height of  triangle  CXD = (2/(2 + 1)) *30  =   (2/3)30 = 20

And the height of triangle AXB =  (1/3)30 = 10

 

Area of triangle   CXD =   (1/2)(40)(20) =  400

Area of triangle AXD = (1/2)(20)(10)  =100

 

And triangles  AXD  and BXC  have equal areas

 

So

 

Area of triangle BXC =    [ 900 - 400 - 100 ] /  2 =    200  units^2

 

 

cool cool cool

 Jul 4, 2022

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