This quadrilateral has two parallel sides, but they are not the same length. There is one right angle. What is it?

Question

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Answer 1

This is a classic definition of a trapezoid! Basically, a quadrilateral with two  parallel sides.

But it's more fun to understand the beauty of special kinds of trapezoids.

The one you described is a "right trapezoid", or "right-angled trapezoid".

If both pair of sides are parallel, it is called a "parallelogram".

If the non-parallel legs are the same length, it is called an "isosceles trapezoid".

One thing I like about trapezoids is one of the ways to calculate the area. The area of a rectangle is the base times the height. The area of a trapezoid is the average length of the bases times the height. This is a cool way to think of it. You can always draw vertical lines to divide the trapezoid into a rectangle and a triangle (or two!), and add up the areas.

I find geometry to be very beautiful, and is a good introduction to the beauty of all of mathematics.