Equilateral Triangle Area Calculator
Calculate the area, perimeter, and other properties of an equilateral triangle using side length or height
Calculate Equilateral Triangle Area
Length of each side of the equilateral triangle
Triangle Properties
Example Calculations
Example 1: Given Side Length
Problem: Find the area of an equilateral triangle with side length 6 cm
Solution:
A = (√3/4) × a²
A = (√3/4) × 6²
A = (√3/4) × 36
A = 0.866 × 36
A = 15.59 cm²
Example 2: Given Height
Problem: Find the area of an equilateral triangle with height 5 inches
Solution:
A = (√3/3) × h²
A = (√3/3) × 5²
A = (√3/3) × 25
A = 0.577 × 25
A = 14.43 in²
Equilateral Triangle Properties
All Angles Equal
Each interior angle = 60°
Equal Sides
All three sides are equal length
Symmetry
3 lines of symmetry
Key Formulas
Area (from side)
A = (√3/4) × a²
Area (from height)
A = (√3/3) × h²
Height
h = (√3/2) × a
Perimeter
P = 3 × a
Quick Tips
An equilateral triangle is also equiangular
It's a special case of an isosceles triangle
Height divides the triangle into two 30-60-90 triangles
Area is approximately 0.433 times the square of the side
Understanding Equilateral Triangles
What is an Equilateral Triangle?
An equilateral triangle is a special triangle where all three sides are equal in length. Because of this property, all three interior angles are also equal, each measuring exactly 60°. The sum of interior angles in any triangle is 180°, so 180° ÷ 3 = 60°.
Special Properties
- •All sides are equal: a = b = c
- •All angles are equal: ∠A = ∠B = ∠C = 60°
- •Has 3 lines of symmetry
- •Centroid, incenter, circumcenter, and orthocenter coincide
Area Formulas Explained
From Side Length
A = (√3/4) × a²
This formula comes from using the general triangle area formula A = (1/2) × base × height, where the height can be calculated using the Pythagorean theorem.
From Height
A = (√3/3) × h²
This formula is derived by expressing the side length in terms of height (a = 2h/√3) and substituting into the side-based formula.
Note: √3 ≈ 1.732, so (√3/4) ≈ 0.433 and (√3/3) ≈ 0.577
Real-World Applications
Architecture
Triangular trusses, roofing structures, and decorative elements
Traffic Signs
Yield signs and warning signs often use equilateral triangle shapes
Engineering
Structural analysis, material distribution, and stability calculations