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Definition: A Trapezoid is a quadrilateral so exactly one pair of parallel (opposite) sides.

A regular trapezoid is a trapezoid whose non-parallel sides are congruent (of equal length).

Interactivity 1 - Trapezoid    Directions for interactivity

Click and drag the slider buttons to change the size. Click and drag point B to move and point А to rotate.

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Basic formulas for a trapezoid with base a , top b and height h is area: A=\frac{a+b}{2} \, h . (Notice no formula for perimeter.)

Examples with the areas of trapezoids

Check the following examples using the above interactivity.

Notice that the length of the sides does not affect the area. We don't even know the length of the right side!
Dimensions of trapezoid Area: A=\frac{a+b}{2} \, h
a b h
10 \,cm 4 \,cm 3 \,cm \frac{10+4}{2} \,cm \cdot 3 \,cm=7 \,cm \cdot 3 \,cm=21 \,cm^2
8 \,mm 5 \,mm 2 \,mm \frac{8+5}{2} \,mm \cdot 2 \,mm=6,5 \,mm \cdot 2 \,mm=13 \,mm^2
0,09 \,m 8 \,cm 30 \,mm \frac{9+8}{2} \,cm \cdot 3 \,cm=8,5 \,cm \cdot 3 \,cm=25,5 \,cm^2
Interactivity 2: Construct a trapezoid
1. Examine the trapezoid in the above interactivity..

2. Now construct a trapezoid with the same properties. If you need help with the steps, click here to open a new window with directions?.

Check whether your construction is stable - Is your construction always a trapezoid no matter what slider or point you move?
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Rules

On the one hand:

  • A trapezoid is completely determined by the lengths of the base, top, height and one of the non-parallel sides.

Comment 1: The area of a trapezoid is determined by the lengths of the base, top and height.
However, there are infinitely many (non-congruent) trapezoids like this.  To see this, in interactivity 1 - change only the length of the left side. This changes the trapezoid, but leaves the area the same!

Comment 2: Determining the perimeter of a trapezoid with only base, top, height and one side is complex since in order to find the length of the other  side we must use trigonometry :).

On the other hand:

  • A trapezoid is completely determined by the lengths of all four sides. See More?.

Comment 3: However, determining the area of such a trapezoid is complex since in order to find the height we must use trigonometry :)

So either we get the area or the perimeter or we have to use trigonometry!

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Page last modified on March 09, 2008, at 10:21 AM