In this section, we will see what is the generic formula that is being used for the calculation of the area of a trapezoid. This is a step-by-step procedure that decomposes the initial problem into smaller problems. Let’s start by the next trapezoid.
We start the method by bringing the two heights from the edges of the smaller base to the bigger base. In our case, we have h1 and h2 from base b to base a. As we can see, the initial trapezoid shape is split into three separate shapes.
- is the left more right triangle
- is the next perpendicular rectangle
- is the right more right tringle
Thus, in order to calculate the whole area of the trapezoid, it is enough to calculate the corresponding areas of the two triangles and the one perpendicular rectangle.
Before we start the procedure, we notice that h1 is equal to h2, thus we can substitute both h1 and h2 with h.
Let’s continue with some mathematics! The trapezoid’s area is the summation of the three separate areas, ae we explained before. Thus, the trapezoid’s area is equal with the left triangle area, plus the central perpendicular rectangle area, plus the right most right triangle area.
We proceed with the necessary substitutions, thus the left more triangle area is h*x1 divided by 2, the central perpendicular rectangle area is b*h and the right most right triangle area is equal with h*x2 divided by 2.
After doing some mathematics we conclude to the relationship 1.
But if we take a more careful look at the relationship1 and bear in mind that the base a is equal to x1 + x2 + b, then the relationship 1 becomes equal to h divided by 2 multiply a + b.
In conclusion, we found the general formula which is used to calculate the area of any trapezoid.
