In a trapezoid ABCD with AB parallel to CD, the diagonals AC and BD intersect at E. What is the ratio of the area of ΔABE to the area of ΔCDE?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. The ratio of AB to CD squared.
In a trapezoid, diagonals divide each other in the ratio of the parallel sides.
AE/EC = BE/ED = AB/CD
Area of triangle = 1/2 × Base × Height
Area(ΔABE)/Area(ΔCDE) = (1/2 × AE × BE)/(1/2 × EC × ED)
= (AB/CD) × (AB/CD)
= (AB/CD)2