# How to Find the Area and Perimeter of a Triangle with Unequal Sides?

A triangle with unequal sides is known as a scalene triangle. Triangles can be classified into several categories depending upon their properties. In this article, we are particularly interested in the various attributes such as perimeter and area of scalene triangle. There are many formulas available to give a measure of the operations mentioned above that we will discuss.

## Classification of Triangles

### Based on Side Length

- Equilateral Triangle – In such a triangle, all the sides are of equal length. An interesting point to note is that all angles measure 60 degrees.
- Isosceles Triangle – In such a triangle, two sides have the same length.
- Scalene Triangle – In this triangle, all three sides are of a different measure. A scalene triangle is one where two sides and two angles are not congruent. For example, the sail of a sailboat is in the shape of a scalene triangle.

### Based on Angle Measure

- Acute Angled Triangle – A triangle in which all three angles measure less than 90 degrees or have only acute angles is called an acute triangle.
- Right Angled Triangle – A triangle in which one angle measures 90 degrees or has a right angle is called a right triangle.
- Obtuse Angled Triangle – A triangle in which one angle measures more than 90 degrees or as an obtuse angle is called an obtuse triangle.

## Area of a Scalene Triangle

The area is defined as the 2D space enclosed within closed boundaries of a figure. Any of the following formulas can be used to find the area depending upon what is known.

### 1. Heron’s Formula

When all three sides are known, we use this formula. Suppose we have a triangle PCN with the measure of sides p, c, and n. Then the Heron’s formula is given by

Semi perimeter s = ( p + c + n) / 2

Area of PCN =

### 2. Height Base Formula

If we have a triangle where we know the measure of one side, and the corresponding perpendicular dropped from the opposite vertice, this formula can be used to find the area.

Area of a triangle = ½ (base)(height)

### 3. Law of Cosines

If you know the length of two sides and the measure of the opposite angle, then this formula can be applied to find the length of the third side. Once the length of the third side is known, then we can use Heron’s formula to find the area of the triangle. Suppose we have a triangle PCN with side lengths given by p, c, n and angles given by P, C, N then according to the law of cosines, the third side is given by

n = p2 + c2 – 2pccosN

## Perimeter of a Scalene Triangle

Perimeter is defined as the total sum of lengths of the boundaries of a figure. If we have a scalene triangle PCN with side lengths given by p, c and n, then the perimeter is given by

Perimeter = Sum of all sides

= p + c + n

## Conclusion

The scope of a topic like triangles is very vast; hence, it is best to join an online educational platform such as Cuemath to help a child with his studying process. At Cuemath, the math experts provide several resources such as worksheets, workbooks, interactive games, and puzzles to supplement their learning. Kids get access to a holistic development environment while being able to maintain their own pace of working. Hopefully, this article gives you an idea of which area formula can be applied to what question, and I wish you all the best!