Hands-on math!


A trapezoid is a quadrilateral with at least 2 opposite sides parallel:

The 2 parallel sides are called the two bases usually designated b1 and b2.
If the other two sides are equal in length it is an isosceles trapezoid.
If you cut off the top of a triangle parallel with it's base, you will have a trapezoid. A square is a special type of trapezoid where the other 2 sides are also parallel (and equal).

To get the area of a trapezoid, first cut it into two triangles diagonally, like this:
Now, you can see that the area of the trapezoid is the sum of the areas of the two triangles you cut it into. The first triangle (A1) has b1 as it's base and the second (A2) has b2 as it's base. They both have the same height (h):
A1 = b1   h / 2
A2 = b2   h / 2
So, the total trapezoid area, A = A1 + A2 = b1 h /2 + b2 h / 2 which is (after grouping terms):
A = (b1 + b2) h / 2
where b1 and b2 are the two parallel bases and h is the height

So here are a couple of problems for you:

1). What is the area of this trapezoid?
Area = _____ sq. ft. 2). What is the height of a trapezoid whose bases are 8 and 6 cm and whose area is 28 sq. cm.?

Height = _____ cm.