Triangle Calculator
Calculate triangle area using Heron’s formula or base and height, perimeter, semi-perimeter, inradius, and classification.
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What Is a Triangle Calculator?
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).
How to Use This Calculator
- Enter side lengths a, b, and c.
- View the calculated area using Heron’s formula, perimeter, inradius, and circumradius.
- Check the geometric classification (equilateral, isosceles, right, or scalene).
Heron’s Area Formula
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.
Worked Example
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
Tips & Key Notes
- Triangle Inequality: The sum of any two sides must be strictly greater than the third side (a + b > c).
- For right-angled triangles, area is simply half the product of the two legs (½ × a × b).
- Inradius is the radius of the largest circle that fits completely inside the triangle: r = A / s.
Frequently Asked Questions
What is Heron’s formula?
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.
What happens if the triangle inequality is violated?
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.
How do you classify a triangle by sides?
Equilateral: all 3 sides equal; Isosceles: 2 sides equal; Scalene: all 3 sides distinct.
What is the semi-perimeter?
The semi-perimeter (s) is half of the total perimeter: s = (a + b + c) / 2.
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