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Triangle Calculator

Calculate dimensions instantly and understand the mathematical steps.

Option A: Base & Height

Unit
Unit

Option B: Three Sides (Heron's Formula)

Perimeter (P) / Semi-perimeter (s)

P: 0.00 | s: 0.00

Triangle Area (A)

0.00

Prefer not to type? Scan values from photo

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Solution Steps (Overview):

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Important Note: All results serve as an indicative guide for academic and practical applications.

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Step-by-Step Guide to Triangle Calculation

1

Step 01

Choose Calculation Method

Select either Base & Height or enter all three side lengths (a, b, c) manually or via photo scan.

2

Step 02

View Instant Results

The calculator instantly computes the total area, perimeter, and semi-perimeter values.

3

Step 03

Understand the Solution Steps

Click the detailed explanation button to see the step-by-step mathematical logic.

4

Step 04

Save or Print Your Solution

Easily copy or print your results for homework, study notes, or practical projects.

Formula Overview for Education and Practice

Mathematical formulas for triangle calculation
Known ValuesArea FormulaPerimeter Formula
Base (b) & Height (h)A = ½ · b · h3 sides required
3 Sides (a, b, c)A = √(s(s-a)(s-b)(s-c))P = a + b + c

Practical Tips & Key Concepts

1. Right-Angled Triangles

For a right-angled triangle, you don't need a separate height measurement. Simply multiply the two perpendicular sides (legs) together and divide by 2.

2. Triangle Inequality

Remember the core rule: the sum of any two side lengths must always be strictly greater than the third side for a valid triangle to form.

3. Semi-Perimeter (s)

The variable 's' in Heron's formula represents exactly half of the total perimeter. Accurate computation of 's' is essential for finding the area.

Frequently Asked Questions

How do you calculate area without knowing the height?

When all three sides (a, b, c) are known, use Heron's formula: A = √(s(s-a)(s-b)(s-c)), where s = (a + b + c) / 2 is the semi-perimeter.

What is the standard formula for triangle area?

The primary formula is A = 0.5 · base · height. It applies to any triangle as long as the height is perpendicular to the base.

What is the Triangle Inequality Theorem?

For three side lengths to form a valid triangle, the sum of any two sides must always be greater than the third side (a + b > c). Our calculator validates this automatically.

Does this work for right-angled triangles?

Yes! In a right-angled triangle, the two perpendicular sides (legs) serve directly as the base and height.

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🎓 Detailed Step-by-Step Explanation

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