Education

# Methods to Find Area of a Scalene Triangle

A triangle is a closed polygon consisting of three sides, three vertices, and three angles. Triangles can be classified into different types depending upon the length of sides and measure of the angles. In this article, we will focus on finding the area of a scalene triangle and other aspects associated with it.

## What is a Scalene Triangle?

A triangle in which all sides are not equal is referred to as a scalene triangle. In other words, a scalene triangle is one in which all sides measure a different length, and all the angles are also of various measures. If the two angles or two sides of a right triangle are not congruent, then it forms a scalene triangle. For example, suppose we have the sail of a sailboat. When the sail is raised, it is likely to create a scalene triangle with all sides having a different measurement.

## Area of a Scalene Triangle

The area of triangle formulas can be used to find the area of a scalene triangle. The area can be explained as the space enclosed by the borders of a figure or the space it occupies in a 2D plane. There are three formulas used to find the area of a scalene triangle.

### 1. Heron’s Formula

When all the three sides of a triangle are known, then we can apply heron’s formula to find the area. It was given by the Heron of Alexandria. Suppose we have a triangle JLR with sides lengths given by j, l, r, then we get:
A =
where, s stands for the semi – perimeter of the triangle and is given by:
s = ( j + l + r) / 2

### 2. Height Base Formula

If we know the measure of one side and the corresponding height dropped from the opposite vertice, we can calculate the area of a triangle by this formula.
Area of a triangle = ½ (base)(height)

### 3. Law of Cosines

Suppose 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 you get this length, all three sides are known; thereby, the heron’s formula can be applied to find the area of a triangle. Suppose we have a triangle JLR with sides given by j, l, r and angles J, L, R. Say we know the length of two sides j, l, and the angle R. Later, by applying the law of cosines, we can find the third side.
r = j2 + l2 – 2jlcosR
Once we find r, it can be used in the heron’s formula to get the area of a triangle.

### Properties of Scalene Triangle

• The sides are not equal.
• The angles are not equal.
• It does not possess a line or point of symmetry.
• The internal angles can be acute, obtuse, or right angles.
• The center of a circumscribing circle will lie inside a triangle if all the angles of the triangle are less than 90 degrees.
• The center of a circumscribing circle will lie outside the triangle if all the angles of the triangle are greater than 90 degrees.

## Conclusion

Depending upon what is known, any of the formulas mentioned above can be used to find the area of a scalene triangle. It is always good practice to avail of the services of a reliable online education platform such as Cuemath to build a solid foundational understanding of the subject. Cuemath helps children to combine fun with studies and provides them with a holistic learning environment. Start your journey of triangles with Cuemath today!