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Trapezoid ABCD has base AB = 20 units and base CD = 30 units. Diagonals AC and BD intersect at X. If the area of trapezoid ABCD is 400 square units, what is the area of triangle BXC?

 Apr 22, 2022
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The height of the trapezoid  can be found as

 

400 = (1/2) (20 + 30)(height)

 

height = 400 / 25  =   16

 

Triangles  AXB  and DXC    are similar

 

And   AB  : DC  =  2 : 3

 

Therefore   the    height of   triangle DXC  =  (3/5) 16  =  9.6

And the height of triangle  AXB  =  (2/5)16  = 6.4

 

So  the combined  areas of these triangles  = 

 

(1/2) ( DC * 9.6  + AB * 6.4)  = 

 

(1/2) ( 30 * 9.6  + 20 * 6.4)   =  208

 

And because of symmetry  triangles AXD and BXC  have the same areas

 

So,  triangle  BXC has an  area of  [ 400 - 208 ]  / 2 =  96

 

cool cool cool

 Apr 22, 2022

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