We have learned how to calculate the areas of a square, rectangle, parallelogram, and circle. In this post, we are going to learn how to find the area of a trapezoid. This is the first post of Finding the Area of a Trapezoid Series.
A trapezoid is a polygon whose exactly one pair of sides are parallel*. The figure below is a trapezoid where sides a and b are parallel.
Notice that if we make another trapezoid which has the same size and shape as above, flip one trapezoid, and make one pair of the non-parallel sides meet, we can form the figure below. That figure is a parallelogram. Can you see why?
Now, observe that the base of the parallelogram from the figure is a + b. Its height is h.
We have learned that the area of a parallelogram is the product of its base and height. So, the expression that describes its area is
Now, when we calculated for the area of the parallelogram above, we actually calculated the area of two trapezoids. Therefore, to get the area of a trapezoid, the have divide the formula above by 2 or multiply it by . That is, if we let be the area of a trapezoid is
where a and b are the base (parallel sides) and h is the height.
*Please take note that there are other definitions of this polygon. In some books, it is defined as polygons whose at least one pair of sides are parallel.
What is the area of a trapezoid whose base are 12 cm and 18 cm and whose height is 15 cm.
Using the notation above, in this problem we have , and ?
The formula for area is
So, substituting we have
So, the area of the trapezoid is 225 square units.
In the next part of this series, we will have more examples on calculating the area of a trapezoid.