Triangle Calculator

Calculate the area of a triangle from base and height.

Area

30

Perimeter

27.6619

Hypotenuse

11.6619

Angle Breakdown

Side Comparison

Angle Breakdown

PropertyValue
Area30.0000
Perimeter27.6619
Hypotenuse11.6619
Angle A30.96°
Angle B59.04°
Angle C90°

Understanding Triangle

The triangle calculator determines the area, perimeter, and other properties of triangles using various methods depending on the information you have available. Triangles are the simplest polygon and one of the most important shapes in mathematics, forming the basis for trigonometry and appearing throughout engineering, architecture, and physics. This calculator supports multiple calculation methods to accommodate whatever measurements you know. If you have the base and height, area is simply half the base times the height. If you have three side lengths, the calculator uses Heron's formula which computes the area from the semi-perimeter. If you have two sides and the included angle, it uses the trigonometric formula. The calculator also determines the triangle type based on sides as equilateral, isosceles, or scalene, and based on angles as acute, right, or obtuse. For right triangles, it connects to the Pythagorean theorem to find missing sides. Understanding triangle calculations is essential for construction, land surveying, navigation, computer graphics, and structural engineering. Every polygon can be decomposed into triangles, making triangle calculations the building blocks for all area computations. Use this free triangle calculator for geometry homework, construction planning, design work, or any situation where you need quick and accurate triangle measurements.

Practical Example

Area = (base × height) / 2. For any triangle: A = ½ × b × h. Where b = base length and h = perpendicular height to that base.

Frequently Asked Questions

How do I find the area of a triangle?

Area = (1/2) × base × height — or use Heron's formula if you only know the side lengths.

What is Heron's formula?

Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2 is the semi-perimeter.

How do I find the angles of a triangle?

Use the law of cosines or law of sines if you know side lengths; angles always sum to 180°.

What if I get a different answer when calculating manually?

First check your order of operations (PEMDAS/BODMAS), then verify your units are consistent. Common errors include rounding too early, sign mistakes, and incorrect formula application. Use this calculator to verify each step of your work.

Are there shortcuts or mental math tricks?

Yes! Many mathematical operations have estimation shortcuts. For example, squaring numbers ending in 5, using the distributive property, or applying benchmark fractions. While shortcuts help with estimates, always use exact calculations for important work.

Disclaimer: This calculator provides estimates for informational purposes only. Actual results may vary. Consult a qualified professional for personalized advice.

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