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?
+128473 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
