How to know the height of a triangle using the area

The height of a triangle can be found in different ways, depending on the type of triangle and the information you have or measure. Right triangles, which include a 90-degree angle, are the easiest to measure using the Pythagorean theorem (if the lengths of two sides are known) or the formula of the area (if the area and the base are known).

The equilateral triangles, in which all sides are of equal length, and the isosceles triangles, in which two of their sides are of equal length, can be cut in half, creating two right triangles. Oblique triangles, those that do not have an interior angle equal to 90 degrees, are more difficult, and require trigonometry to find their height. Next, we will calculate the height of a right triangle using the area formula.

Steps to follow:

one

The first thing you have to do to calculate the height of a triangle you know its area is to draw the triangle and write on the sides and the known values ​​such as the area and sides.

two

Then write the formula of the area of ​​a triangle, A = (b · h) / 2, where A = area, b = base and h = height.

3

Now substitute in the formula all the values ​​you know, that is, the area and base of the triangle to try to find the height, so that:

72 (the area of ​​the triangle) will be equal to the multiplication of 18 times the height, all divided by two.

4

The next step will be to clear the h (height) in order to know its value, so remember that what you are multiplying passes to the other side of the equal dividing and vice versa.

So, we passed the 2 that was dividing to multiply it by the 72 and we performed the operation and then the 18 that multiplied will go to divide. When we finish the calculations, we discover that the value of h is 8.

Therefore, the height of the triangle is 8 cm.

5

If you want to do the check to be sure that you have done well, you will only have to replace the value of the height next to those you already knew in the formula to calculate the area of ​​the triangle.

In this way, when doing the mathematical operations, we obtain that in both cases the value of the area is 72 cm², so it is correct.