In trapezoid ABCD the lengths of the bases AB and CD are 8 and 17 respectively. The legs of the trapezoid are extended beyond A and B to meet at point E. What is the ratio of the area of triangle EAB to the area of trapezoid ABCD?
+128408 We wil have a larger triangle CDE and a smaller triangle BAE
And these triangles are similar because AB is parallel to CD
Since AB / CD = 8 /17
Then 8/17 is the scale factor of triangle BAE to triangle
Let A be the area of CDE.....
Then the area of BAE = (8/17)^2 CDE = (64/289)CDE = (64/289)A
So....the area of the trapezoid ABCD =
Area of CDE - Area BAE =
A - (64/289)A = (225/289)A
So the ratio of triangle EAB to trapezoid ABCD =
(64/289)A / [ (225/289) A ] =
64 /225
