Geometry Puzzle – Challenge 59
Geometry Puzzle – Challenge 59 is a multiple-choice math challenge from Effortless Math. Read the problem, choose from the answer options below, then open the solution to see the full step-by-step working and check your reasoning against it.
Challenge
The figure shows parallelogram ABCD with A and B along the top, C and D along the bottom, and point E on side CD. Segments are drawn from A to E and from A to D.
In the figure above, ABCD is a parallelogram and point E is the midpoint of CD. What is the ratio of the area of triangle ADE to parallelogram ABCD?
A- 1: 2
B- 1: 3
C- 1: 4
D- 1: 6
E- it cannot be determined
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The correct answer is C.
AD divides the parallelogram in half. AE divides the half parallelogram into half again. Because the heights of triangles ACE and ADE are equal and their bases are equal.
Triangle ADE is, therefore, one fourth of the parallelogram. And the ratio is 1: 4
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