Triangle Area and Perimeter Calculator
Find the area or perimeter of any triangle by entering its three side lengths. Ideal for geometry homework, construction projects, or land measurement tasks.
About this calculator
This calculator uses Heron's Formula to compute a triangle's area from its three side lengths (a, b, c). First, the semi-perimeter is calculated: s = (a + b + c) / 2. Then the area is found using: Area = √(s × (s − a) × (s − b) × (s − c)). The perimeter is simply the sum of all three sides: P = a + b + c. Heron's Formula is powerful because it requires no angle measurements — just the three side lengths. It works for any valid triangle, whether scalene, isosceles, or equilateral, as long as the triangle inequality is satisfied (each side must be less than the sum of the other two).
How to use
Suppose your triangle has sides a = 5, b = 6, and c = 7 units. First compute the semi-perimeter: s = (5 + 6 + 7) / 2 = 9. Then apply Heron's Formula: Area = √(9 × (9 − 5) × (9 − 6) × (9 − 7)) = √(9 × 4 × 3 × 2) = √216 ≈ 14.70 square units. For the perimeter, simply add the sides: P = 5 + 6 + 7 = 18 units. Enter those three values, select your calculation type, and the result appears instantly.
Frequently asked questions
How do I calculate the area of a triangle if I only know the three side lengths?
You can use Heron's Formula, which requires only the three side lengths. Calculate the semi-perimeter s = (a + b + c) / 2, then compute Area = √(s(s−a)(s−b)(s−c)). This approach avoids the need for any angle measurements. It is especially useful in surveying and construction where angles are hard to measure directly.
What is the difference between the area and perimeter of a triangle?
The perimeter is the total distance around the triangle — the sum of all three side lengths (P = a + b + c). The area measures the two-dimensional space enclosed within the triangle, expressed in square units. They serve different purposes: perimeter is used for fencing or framing, while area is used for surface coverage like flooring or painting. Both are fundamental properties in geometry and real-world applications.
When does a set of three side lengths not form a valid triangle?
Three sides form a valid triangle only if each side is strictly less than the sum of the other two — this is called the triangle inequality theorem. For example, sides 1, 2, and 10 do not form a triangle because 1 + 2 < 10. If this condition is violated, Heron's Formula will produce a negative value under the square root, which has no real solution. Always verify the triangle inequality before computing area or perimeter.