Triangle Area Calculator

Math: Triangle Area Calculator

The Triangle Area Calculator is designed to help you find the area, sides, angles, and perimeter of a triangle based on the values you know. Triangles come in many shapes and sizes, but they all have one thing in common: they have three sides. Whether you're dealing with an equilateral, isosceles, or scalene triangle, our calculator is here to help.

How to calculate the area of a triangle?

The area (A) of a triangle can be found using different formulas depending on the known values:

1. When the base and height are known:

The simplest and most common formula for the area of a triangle is:

Area = 0.5 * base * height

2. When all sides (a, b, c) are known (Heron's formula):

First, calculate the semi-perimeter (s) as follows:

s = (a + b + c) / 2

Then, the area can be found using Heron's formula:

Area = sqrt(s * (s - a) * (s - b) * (s - c))

3. When two sides and the included angle are known:

If you know two sides of the triangle and the angle between them (let's call the sides a and b, and the angle γ), you can use the following formula:

Area = 0.5 * a * b * sin(γ)

Other Triangle Calculations:

In addition to the area, you might also be interested in finding the sides, angles, and perimeter of a triangle. Here's how:

1. Pythagorean theorem:

Used to find the length of a side in a right-angled triangle:

c² = a² + b²

2. Trigonometric functions:

Used to find angles or sides in any triangle:

sin(α) = a/c, cos(α) = b/c, tan(α) = a/b

3. Triangle inequality theorem:

Used to check if a triangle is valid:

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

4. Perimeter:

The perimeter of a triangle is simply the sum of its sides:

Perimeter = a + b + c