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HOW IS THE AREA OF ​​THE TRAPEZOID CALCULATED?

To find the area of a trapezoid, we start from the rule, which is: the size of ​​the triangle is calculated by multiplying the sum of the two bases by the height and then dividing the result obtained by two.

Don’t be scared! Now we explain why …

A (trapezoid) = (b + B) xh: 2

Ok: this if you need to know the rule by heart, but how to understand how to calculate the area of ​​the trapezoid?

Let’s start from the rule:

The area of ​​the triangle is calculated by multiplying the sum of the two bases by the height and divides it into two

However, don’t give up because, with an easy example, you will understand why.

METHOD OF FIND THE AREA OF A TRAPEZOID

Take a piece of paper, fold it in half and draw a trapezoid on it.

Keeping the Foglio tightly together, cut the trapezoid along the outline. You will get two CONGRUENT trapezoids.

Now rotate one of the two trapezoids, as in the image below, to build a parallelogram.

The base of the parallelogram obtained is equal to the sum of the trapezoid’s two floors (b and B), and the height is the same as the trapezoid.

SO HOW TO CALCULATE THE KEYSTONE AREA?

Calculating the area of ​​the parallelogram and then dividing it by two.

Is the area of ​​the parallelogram calculate based on height? We know the basis! It is the sum of b and B.

So we add b (minor base) times B (significant base). Then we multiply by the height, and we get the area of ​​the whole parallelogram. But we need that of the trapezoid. So we will divide it by two. 

Let’s try an exercise now?

Self…

b = 6 cm

B = 8 cm

h = 4 cm

Here’s where the (b + B) xh rule comes from: 2

To finish: if you know the area and want to calculate the sum of its bases or the height, here is what you can do.

b + B = A x 2: hh = A x 2: (b + B)

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