Lesson 2: Area - Area of Trapezoids

   Constructing Knowledge

A trapezoid is a four-sided polygon with two parallel sides and two other sides that are not parallel. Calculating the area of a trapezoid involves its height and both bases (the lengths of the parallel sides).



Calculating the area of a trapezoid can be done by splitting the trapezoid into two triangles. If a Trapezoid is cut into two triangles, their areas can be calculated and added together to give the area of the trapezoid.





Recall that the formula for the area of one triangle is \(\text{A}_{\text{triangle}}=\frac{bh}{2}\)

Also, recall that the height of a triangle may be outside of the triangle, as in Triangle 2.

\(\text{A}_{\text{triangle}}=\frac{bh}{2}\)

added to

\(\text{A}_{\text{triangle}}=\frac{ah}{2}\)

If we combine both of these formulas together we get:

\(\text{A}_{\text{trapezoid}}=\frac{ah}{2}+\frac{bh}{2}\)

Now we can add the fractions together because both have a denominator of 2.

\(\text{A}_{\text{trapezoid}}=\frac{\left(ah\right)+\left(bh\right)}{2}\)

Factoring is not a concept taught in this course, however we can now factor out the 'h' (you may recall doing something like this in junior high).

\(\text{A}_{\text{trapezoid}}=\frac{h\left(a+b\right)}{2}\)

In this formula, a and b are the lengths of the parallel sides.


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