Area of a trapezoid - derivation
This page describes how to derive the forumula for the
area of a trapezoid by creating a
from two congruent trapezoids.
The formula is simply one half the area of this parallelogram.
- Start with a trapezoid with known base lengths (b1, b2) and altitude (height).
- Make a copy of it.
- Rotate the copy 180°.
- Translate (move) the copy to touch the original.
Click on the "Run" button below to see this in action.
When the two trapezoids are combined in this way, the result is a
which has two pairs of opposite, congruent sides.
Recall that the
area of a parallelogram
is its altitude (h) times the length of either base.
From the figure above we see that both base lengths are equal to b1+b2.
So the area of the parallelogram is
Since this is the area of two trapezoids we have to divide this by two, giving
This can be rearranged into more familar forms:
Related polygon topics
Types of polygon
Area of various polygon types
Perimeter of various polygon types
Angles associated with polygons
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