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?
+128474 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
