Equilateral Triangle Calculator

How to Calculate Equilateral Triangle Properties

An equilateral triangle is a special type of triangle where all three sides have equal length and all three angles are 60°. This unique geometry allows for straightforward calculations of various properties once you know one of its dimensions.

Equilateral Triangle Formulas

Let \( a \) be the side length of the equilateral triangle. Then:

• Height (h): \( h = \frac{a\sqrt{3}}{2} \)
• Area (A): \( A = \frac{a^2\sqrt{3}}{4} \)
• Perimeter (P): \( P = 3a \)
• Inradius (r): \( r = \frac{a}{2\sqrt{3}} \)
• Circumradius (R): \( R = \frac{a}{\sqrt{3}} \)

Calculation Steps

1. Identify the known value (side length, height, area, perimeter, inradius, or circumradius)
2. If the known value is not the side length, use the appropriate formula to calculate the side length
3. Use the formulas above to calculate all other properties

Example Calculation

Let's calculate the properties of an equilateral triangle with a side length of 5 units:

1. Side length (a) = 5 units
2. Height: \( h = \frac{5\sqrt{3}}{2} \approx 4.33 \) units
3. Area: \( A = \frac{5^2\sqrt{3}}{4} \approx 10.83 \) square units
4. Perimeter: \( P = 3 \cdot 5 = 15 \) units
5. Inradius: \( r = \frac{5}{2\sqrt{3}} \approx 1.44 \) units
6. Circumradius: \( R = \frac{5}{\sqrt{3}} \approx 2.89 \) units

Visual Representation

Here's a visual representation of an equilateral triangle:

This diagram illustrates the key features of an equilateral triangle, including its side lengths, height, and angles.