Education

# How to Find the Area of an Equilateral Triangle and Isosceles Triangle?

A triangle is a closed polygon that has three sides, three angles, and three vertices. When the length of the three sides of a triangle is equal, it is known as an equilateral triangle. The three angles of an equilateral triangle are equal and measure 60 degrees each. There are several concepts associated with it such as properties, perimeter, and area of equilateral triangle. Let us take a look at the methods to calculate the area of an equilateral triangle.

### 1. Heron’s Formula

This formula can be used to calculate the area of any triangle if all three sides are known. It requires us first to find the semi perimeter of the triangle and then to use this to find the area. Suppose we have a triangle with side lengths given by j, t, l then.

• Semi perimeter, s = (j + t + l) / 2
• Area of the triangle = √[s (s – j) (s – t) (s – l)]

However, as in an equilateral triangle, all sides are equal; thus, let us suppose that the side length is d. Thus, the above formula can be substituted with this value to get the area as follows.

• Semi perimeter of equilateral triangle = 3d/2.
• Area of equilateral triangle = √3d2/4.

### 2. Base Height Formula

If we drop a perpendicular from one vertice of the triangle to the opposite side, it forms the height, and the corresponding side is the base. To calculate the area of the triangle, the formula is given by

Area of a triangle = ½ × (base) × (height)

For an equilateral triangle, we can easily find the height by using the Pythagoras theorem. The height divides the base into two halves; thus, we can apply the theorem to get the height. Let the side length be equal to d of an equilateral triangle, then

• Height = √3d/2
• Area = ½ (d)(√3 d/2) = √3d2/4

## What is an Isosceles Triangle?

A triangle in which two sides are of equal length is known as an isosceles triangle. This also implies that the two angles opposite to the equal sides are equal.

The area of isosceles triangle formula can be given by two methods similar to the ones discussed above.

### 1. Heron’s Formula

Let the length of equal sides of the triangle be given by m, and the third side measures n. Then by substituting these values in the heron’s formula, we get

• Semi perimeter s = (m + m + n)/2
• Area of an isosceles triangle = n/2 ×  √[m2 – n2/4]

### 2. Base Height Formula

We can find the height of the triangle by the Pythagoras theorem and use this value to find the area.

• Height = m
• Area of an isosceles triangle = ½ m2.

## Conclusion

There are other methods to find the area of triangles, including trigonometric formulas. Kids can get confused about finding the area of a given triangle using manipulations; hence, they should join an online educational institution such as Cuemath to combat this confusion. At Cuemath, the certified experts use various methods to teach kids in a way that makes the subject approachable. They use resources such as workbooks, worksheets, math puzzles, etc., to improve the level of engagement. Most importantly, they place immense focus on building a robust mathematical foundation so that a child can successfully attempt any level of problem. Hopefully, this article helps you to understand triangles better, and I wish you all the best!
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