Area of Triangle Calculator

Area of Triangle Calculator

Understanding Triangle Area Calculation

The area of a triangle represents the total space enclosed within its three sides. Depending on the information you have available (such as the base and height or the lengths of all three sides), different mathematical formulas are used to find the result.

The Classic Formula: Base times Height

This is the most common method used when you know the length of one side (the base) and the perpendicular distance from that side to the opposite vertex (the height).

Area = ½ × Base × Height

Example: If a triangle has a base of 10 cm and a height of 5 cm, the area is 0.5 × 10 × 5 = 25 square centimeters.

Heron's Formula: When You Only Know the Sides

If you don't know the height but you know the lengths of all three sides (a, b, and c), you can use Heron's Formula. First, calculate the semi-perimeter (s):

s = (a + b + c) / 2

Then, use the area formula:

Area = √[s × (s – a) × (s – b) × (s – c)]

Note: For a valid triangle, the sum of any two sides must always be greater than the third side.

Why Calculate Triangle Area?

Calculating the area of a triangle is essential in various fields including architecture, engineering, and land surveying. Whether you are determining the amount of fabric needed for a sail, the roofing area for a gabled house, or solving complex geometric proofs, this calculator provides instant and accurate results.