Calculate triangle area using Heron’s formula or base and height, perimeter, semi-perimeter, inradius, and classification.
Did this calculation save you time?
Student ProjectHi! I'm a student developer building Calculat in my spare time. I was tired of searching for basic math tools and having to click through 10 spammy popups, loan ads, and cookie trackers.
I keep this website 100% free, private, and ad-free. If this helped you with your homework, project, or finances today, bookmarking this page or telling a friend helps me keep building more free tools!
A triangle is a fundamental three-sided polygon with three vertices and interior angles summing to 180°. Triangles are classified by side lengths (equilateral, isosceles, scalene) or by internal angles (acute, right, obtuse).
s = \frac{a+b+c}{2}, \quad A = \sqrt{s(s-a)(s-b)(s-c)}Heron’s formula calculates the area of any valid triangle using only the lengths of its three sides and the semi-perimeter s.
Scenario: Find area of a triangle with sides a = 7, b = 8, c = 9
Perimeter: P = 7 + 8 + 9 = 24
Semi-perimeter: s = 24 / 2 = 12
Heron’s formula: A = √(12 × (12 - 7) × (12 - 8) × (12 - 9))
A = √(12 × 5 × 4 × 3) = √720 ≈ 26.8328
Heron’s formula allows you to calculate the area of any triangle when all three side lengths are known, without needing to know any angles or perpendicular heights.
If the sum of two sides is less than or equal to the third, the sides cannot connect in 2D space to form a closed triangle.
Equilateral: all 3 sides equal; Isosceles: 2 sides equal; Scalene: all 3 sides distinct.
The semi-perimeter (s) is half of the total perimeter: s = (a + b + c) / 2.
Solve right triangles with hypotenuse, legs, area, perimeter, altitude, and acute angles using trigonometry and the Pythagorean theorem.
Solve a² + b² = c² for missing hypotenuse or leg with step-by-step radical simplification and exact decimal solutions.
Calculate rectangle area, perimeter, diagonal, and aspect ratio from length and width with complete mathematical steps.