Calculating the Area of an Equilateral Triangle | Explained Step by Step

Area of equilateral triangle

The area of an equilateral triangle can be calculated using the formula:
Area = (sqrt(3) / 4) * side^2

In this formula, “sqrt(3)” represents the square root of 3, and “side” refers to the length of one side of the equilateral triangle

The area of an equilateral triangle can be calculated using the formula:
Area = (sqrt(3) / 4) * side^2

In this formula, “sqrt(3)” represents the square root of 3, and “side” refers to the length of one side of the equilateral triangle.

To understand why this formula works, let’s break it down:

1. The first step is to find the height of the equilateral triangle. The height is a line segment that forms a right angle with one side of the triangle and connects the opposite vertex. In an equilateral triangle, the height bisects the base and creates two identical right-angled triangles.

2. The height of an equilateral triangle can be found using a special relationship between the side length and the height. By drawing a line segment from the vertex to the midpoint of the base, you create a right-angled triangle. This right-angled triangle is a special type called a 30-60-90 triangle. In this triangle, the hypotenuse (the side opposite the right angle) is twice the length of the shorter leg (the height), and the longer leg (half of the base) is the square root of 3 times the shorter leg.

3. Therefore, the height of an equilateral triangle can be calculated as: height = (sqrt(3) / 2) * side

4. Once we have the height, we can calculate the area using the formula for the area of a triangle: Area = (base * height) / 2. In an equilateral triangle, the base is the same length as the side. Substituting the values, we get: Area = (side * (sqrt(3) / 2) * side) / 2 = (sqrt(3) / 4) * side^2

So, to find the area of an equilateral triangle, you can use this formula: Area = (sqrt(3) / 4) * side^2, where “side” represents the length of any one side of the equilateral triangle.

More Answers: