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This is Nancy ET Johnson, mathematics teacher. This is how to find the height of a trapezoid.
First we're going to look at how to find the area of a trapezoid and then we'll work backwards
to find the height. In order to find the area of a trapezoid we're going to cut it in half
to show that it will form a parallelogram whose area is much easier to find. We'll cut
our trapezoid, here, halfway between base one and base two. Once we've cut our trapezoid
in half, we're going to take the top part and move it and turn it so that base one and
base two together now form the base of this long parallelogram. The height of our new
parallelogram is only half the height of our trapezoid. Therefore, the area of the trapezoid
is base one plus base two, times half the height. If base one were twelve and base two
were eight, and the height of the original trapezoid was six, then we would need to take
twelve plus eight, the two bases, add those together, twenty, and then multiply it times
half of the original height. Original height six, half of it is three, so twenty times
three gives us an area of sixty for our trapezoid. That's how to find the area of a trapezoid
but we wanted to know how to find the height. If you want to find the height you need to
work backwards from the area, sixty, divide by the two bases and multiply by two. So we're
going to just work backwards. Let's look at an example. Here's how to work backwards using
the same numbers we used in finding the area of the trapezoid. If our area is sixty and
our two bases are twelve and eight, our formula is area is one half of base one plus base
two, times the height. We substitute sixty for the area, twelve and eight for the bases,
we're trying to figure out the height. This becomes twelve plus eight, twenty, half of
twenty is ten, so sixty equals ten times the height. Ten times six is sixty. So the height
is six.
That's how to find the height of a trapezoid. I'm Nancy ET Johnson, mathematics teacher.