The area of an equilateral triangle helps us measure the space inside a triangle where all three sides are equal and every angle is exactly 60°. Because of its symmetry, this triangle has a very simple area formula that depends only on the side length. This makes it a favourite in geometry, design, and competitive exam questions. The formula is quick, direct, and useful in many real-life applications such as tiling, land measurement, and architectural layouts.
Formula for Calculating the Area of an Equilateral Triangle – Overview
| Formula | Variables & Meaning | When It Is Used |
|---|---|---|
| A = (√3 / 4) × a² | a = side length, √3 ≈ 1.732 | Used only when the triangle is equilateral (all sides equal) |
What is the Area of an Equilateral Triangle in Maths?
In mathematics, the area of an equilateral triangle represents the total region covered within a triangle whose sides are all equal and angles are 60°. This formula is much simpler than Heron’s formula because it only requires the side length.
The height of an equilateral triangle is derived using the Pythagoras theorem:
Height = (√3 / 2) × a.
Substituting this into the basic area formula:
Area = ½ × base × height
gives:
Area = ½ × a × (√3 / 2 × a)
= (√3 / 4) × a².
This is why the formula works so efficiently. It is commonly used in geometry problems, CUET, JEE, SSC, Banking exams, and even in real-life tasks such as designing tiles, dividing land, and creating triangular structures.
Examples to Calculate Area of an Equilateral Triangle
Example 1: Side = 6 cm
Step 1: A = (√3 / 4) × a²
Step 2: A = (√3 / 4) × 6²
Step 3: A = (√3 / 4) × 36
Step 4: A = 9√3 ≈ 15.59 cm²
So, the area of an equilateral triangle with side 6 cm is 15.59 cm².
Example 2: Side = 10 m
Step 1: A = (√3 / 4) × a²
Step 2: A = (√3 / 4) × 10²
Step 3: A = (√3 / 4) × 100
Step 4: A = 25√3 ≈ 43.3 m²
So, the area of an equilateral triangle with side 10 m is 43.3 m².
FAQs about Area of an Equilateral Triangle Formula
Q1. What is the formula for the area of an equilateral triangle?
A = (√3 / 4) × a², where a is the side length.
Q2. Can I use Heron’s formula for equilateral triangles?
Yes, but the direct formula is much quicker and easier.
Q3. Why does √3 appear in the formula?
It comes from calculating the triangle’s height using the Pythagoras theorem.
Q4. Where is this formula used in real life?
In architecture, tiling patterns, construction, land measurement, and design work.
Q5. Is this formula important for exams?
Yes, it is frequently asked in CBSE, CUET, JEE, SSC, and Banking exams.
Q6. What makes an equilateral triangle special?
All sides are equal, and every angle is exactly 60°.