Scalene Triangle

1 Star2 Stars3 Stars4 Stars5 Stars (No Ratings Yet)
Loading...

Scalene triangle drawing

A scalene triangle is a triangle in which all three sides have different lengths and all angles are diferent too.

This type of triangle can be a right triangle (one angle with measure 90°) but not all scalene triangles have a right angle. The scalene triangles can be acute (all interior angles measuring less than 90°), obtuse (one interior angle measuring more than 90°) or right triangles depending on their angles.

These three interior angles add to 180° (α+β+γ=180º) as in all of triangles.

Why do the angles of a triangle add up to 180°?

Area of a Scalene Triangle

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.

Perimeter of a Scalene Triangle

A scalene triangle is a triangle in which all three sides are in different lengths. The perimeter of a scalene triangle with three unequal sides is determined by adding the three sides.

If we know the length of the three sides you can calculate its perimeter using the following formula:

Formula for the perimeter of a scalene triangle

If only the length of two sides and the angle between them are given, in order to find the perimeter we need to calculate the other side using the Law of Cosines (Cosine Rule):

Formula for the perimeter of a scalene triangle knowing two sides and an angle

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.

Solved Exercises

Exercise of the Area of a Scalene Triangle

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.

Exercise of the Perimeter of a Scalene Triangle

Consider a given triangle:

Exercise 1 of scalene triangle to calculate its perimeter

Let be a scalene triangle of known sides, these being a=2 cm, b=4 cm y c=3 cm.

What is its perimeter? This will be calculated as the sum of its three sides.

Calculating the perimeter of a scalene triangle

So, the perimeter is 9 cm.

Exercise 3

Drawing of exercise 2 of the perimeter

What is its perimeter?

Solution:

In this triangle we only know two sides (a=4 cm y c=6 cm) and the angle they form (B=85°). First we have to find the length of side b.

For this we use the Law of Cosines:

Calculation of side b in exercise 2

So, we get the side b=6.92 cm.

Now we can calculate the perimeter by adding the three sides of the triangle:

Result in exercise 2

The perimeter of the triangle is 16.92 cm.


AUTHOR: Bernat Requena Serra

YEAR: 2020


IF YOU LIKED IT, SHARE IT!

Leave a Reply

Your email address will not be published. Required fields are marked *