Area of a scalene triangle

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Drawing of the scalene triangle

The area of a scalene triangle can be calculated using Heron’s formula if all its sides (a, b and c) are known.

Formula for the area of a scalene triangle

It could also be calculated if a side (b) is known and the height (h) associated with that side.

Drawing of the scalene triangle with a known side and height

Formula for the area of a scalene triangle knowing one side and the associated height

Finally, the area of a scalene triangle can also be calculated by trigonometric procedures, provided that three elements of the triangle are known, at least one of which is a side.

Download this calculator to get the results of the formulas on this page. Choose the initial data and enter it in the upper left box. For results, press ENTER.

Triangle-total.rar         or   Triangle-total.exe      

Note. Courtesy of the author: José María Pareja Marcano. Chemist. Seville, Spain.

Exercise

Example of a scalene triangle with known sides

Find the area of the scalene triangle given its three sides: a=2 cm, b=4 cm and c=3 cm.

What is its area?

We can calculate the area using Heron’s formula. First, we have to determine the semiperimeter s:

Calculation of the semiperimeter of a scalene triangle to obtain its area

Now, we can apply the Heron’s formula:

Calculation of the area in exercise 1

So the area is 2.9 cm2.

Table of Triangle Area Formulas

You can see the table of triangle area formulas . Depending on the type of triangle you may need one element (scalene triangle), two (base and height) or three (as long as they are not the three angles).

Table of triangle area formulas for the reasons we know

AUTHOR: Bernat Requena Serra

YEAR: 2020


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