Area Of Trapezoids
Hello there. This math post is on finding the area of trapezoids.
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Topics
- What Is A Trapezoid?
- The Formula For The Area Of A Trapezoid
- Worked Out Examples
What Is A Trapezoid?
A trapezoid is a quadrilateral (four sided shape) with one pair of opposite parallel sides. If this pair of opposite sides were to extend they would not touch each other. This pair of sides are referred to as the bases for the trapezoid. The other two sides which are not parallel are referred to the legs of the trapezoid.
Here are some picture example of trapezoids (Found from DuckDuckGo Image Search):
The Formula For The Area Of A Trapezoid
Looking at the area of a trapezoid formula does look scary at first. If you look at more closely, it is similar to the area of a triangle.
The area of a triangle is the base multiplied by the height divided by two.
The area of the trapezoid is the two bases added together first which is then multiplied by the height of the trapezoid and divided by two.
Worked Out Examples
The images are screenshots from me using https://www.mathsisfun.com/geometry/drawing.html.
Example One - Simple Case
Given this picture, what is the area of this trapezoid?
Answer
We have the two bases length and the height of the trapezoid. It is a simple problem where you substitute the right values in the area of the trapezoid formula accordingly.
Example Two - Multi Step Problem
Knowing that the perimeter of this trapezoid is 12 units, what is the area of this particular trapezoid?
Answer
The area of the trapezoid cannot be used right away as the height is unknown. Finding the height in this case is easy as we have the perimeter information and the other sides to conclude that the height length is 1 unit. Compute the area is as follows:
Example Three - Known Area, Unknown Height
Given that this trapezoid is 12 square units with one base being 5 units and the second base being 7 units, what is the trapezoid's height?
Answer
This trapezoid's height is 2 units.
Notes
A natural extension for these area of trapezoid problems would be to add in Pythagorean Theorem into the mix. I didn't do that here.
Another variation for the problems is to add in polynomials and quadratics factoring from high school mathematics.