Triangle Area Calculator
Free Triangle area Calculator for triangle. Enter values to get step-by-step solutions with formulas and graphs. See charts, tables, and visual results.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Area = ½ × base × height
A triangle's area equals half the product of its base and the perpendicular height measured from that base to the opposite vertex — a direct consequence of every triangle being exactly half of a parallelogram sharing the same base and height.
Worked Examples
Example 1: Basic base and height
Problem:A triangular garden bed has a base of 6 meters and a height of 4 meters. Find its area.
Solution:Area = ½ × base × height = ½ × 6 × 4 = 12.
Result:Area = 12 square meters
Example 2: Triangular roof section
Problem:A gable roof triangle has a base of 9 meters and a height of 3.5 meters. How much roofing material (area) is needed for that section?
Solution:Area = ½ × 9 × 3.5 = ½ × 31.5 = 15.75.
Result:Area = 15.75 square meters
Frequently Asked Questions
Why is the triangle area formula 'half of base times height'?
Any triangle is exactly half of a parallelogram that shares the same base and height — you can prove this by duplicating the triangle, rotating the copy 180 degrees, and joining it to the original along one side to form a parallelogram with area base × height. Since a parallelogram's area is base × height, each of the two identical triangles that make it up must be exactly half of that.
Which measurement counts as the 'height' of a triangle?
The height (or altitude) is the perpendicular distance from the chosen base to the opposite vertex — not the length of a slanted side. For an obtuse triangle, the height may fall outside the triangle itself, meaning the foot of the perpendicular lands on the extension of the base line rather than between its endpoints, but the formula still applies exactly the same way.
How do I find a triangle's area if I only know the three side lengths, not the height?
Use Heron's Formula: compute the semi-perimeter s = (a+b+c)/2, then Area = √[s(s−a)(s−b)(s−c)]. This avoids needing to measure or calculate a perpendicular height directly and works for any triangle given just its three side lengths.
How is triangle area calculated using two sides and the included angle?
When you know two sides (a, b) and the angle C between them, the area is Area = ½ × a × b × sin(C). This trigonometric form is especially useful in surveying and navigation, where angles are often easier to measure directly than perpendicular heights.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy