Geometry Guide P. 20, #12

[Q]

How is AE the height of the Trapezoid - doesn't make sense to me? Thanks in advance.

[rfernandez]

Notice that AD is parallel to CE because ABCD is a rhombus. Also, notice that angle AEC is 90 degrees. Therefore, AE is the perpendicular distance between the parallel sides of the trapezoid.

The orientation of the figure makes it hard to see at first, but try covering up triangle ABE with a sheet of paper and then rotate the page such that CE is horizontal. You'll see that in fact the drawing is in pretty good scale.

[jay.mathew]

I've always been able to see the trapezoid (I think), but I can't understand how AE is the height. To me, AB or DC look more like height (10).

Are there any other ways to look at it?

[Ben Ku]

Hi Mathew,

In the Geometry Strategy Guide (4th edition), page 20 question 21, AB and DC are the sides of the rhombus, but not the height. Remember that the height of a rhombus (and any parallelogram) is the PERPENDICULAR distance between two opposite sides. AE is a height because it starts from point A to point E, and is perpendicular to the sides AD and BC. See page 16 under Parallelogram to see the height drawn.

Hope that helps!