Tri Calculator

Triangle Area & Perimeter Calculator

function calculateTriangle() { var sideA = parseFloat(document.getElementById('sideA').value); var sideB = parseFloat(document.getElementById('sideB').value); var sideC = parseFloat(document.getElementById('sideC').value); var resultDiv = document.getElementById('result'); if (isNaN(sideA) || isNaN(sideB) || isNaN(sideC) || sideA <= 0 || sideB <= 0 || sideC sideC) && (sideA + sideC > sideB) && (sideB + sideC > sideA))) { resultDiv.innerHTML = 'The given side lengths do not form a valid triangle (Triangle Inequality Theorem).'; return; } // Calculate Perimeter var perimeter = sideA + sideB + sideC; // Calculate Area using Heron's Formula var s = perimeter / 2; // Semi-perimeter var area = Math.sqrt(s * (s – sideA) * (s – sideB) * (s – sideC)); resultDiv.innerHTML = '

Triangle Properties:

' + 'Perimeter: ' + perimeter.toFixed(2) + ' units' + 'Area: ' + area.toFixed(2) + ' square units'; }

Understanding the Triangle Area & Perimeter Calculator

A triangle is one of the most fundamental shapes in geometry, a polygon with three edges and three vertices. Its properties are crucial in various fields, from architecture and engineering to physics and computer graphics. This calculator helps you quickly determine two key properties of any triangle: its perimeter and its area, given the lengths of its three sides.

What is a Triangle?

At its core, a triangle is a closed, two-dimensional shape with three straight sides and three angles. The sum of the interior angles of any triangle always equals 180 degrees. Triangles can be classified by their side lengths (equilateral, isosceles, scalene) or by their angles (right, acute, obtuse).

Calculating the Perimeter

The perimeter of any polygon is simply the total length of its boundary. For a triangle, this means adding up the lengths of its three sides. If a triangle has sides of length 'a', 'b', and 'c', its perimeter (P) is given by the formula:

P = a + b + c

The perimeter is measured in linear units (e.g., meters, feet, inches).

Calculating the Area (Heron's Formula)

The area of a triangle represents the amount of two-dimensional space it occupies. While the most common formula for area is (1/2) * base * height, this requires knowing the height, which isn't always readily available. When you know all three side lengths, Heron's Formula provides an elegant way to calculate the area:

1. First, calculate the semi-perimeter (s), which is half of the perimeter:

   s = (a + b + c) / 2

2. Then, use the semi-perimeter in Heron's Formula to find the area (A):

   A = √(s * (s – a) * (s – b) * (s – c))

The area is measured in square units (e.g., square meters, square feet, square inches).

The Triangle Inequality Theorem

An important principle in geometry is the Triangle Inequality Theorem. It states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This theorem ensures that the three given side lengths can actually form a closed triangle. If this condition is not met, the sides cannot connect to form a valid triangle.

• a + b > c
• a + c > b
• b + c > a

Example Calculation

Let's say you have a triangle with side lengths:

• Side A = 3 units
• Side B = 4 units
• Side C = 5 units

Using the calculator:

1. Perimeter: P = 3 + 4 + 5 = 12 units
2. Semi-perimeter (s): s = 12 / 2 = 6 units
3. Area: A = √(6 * (6 – 3) * (6 – 4) * (6 – 5)) = √(6 * 3 * 2 * 1) = √36 = 6 square units

This particular triangle is a right-angled triangle, and its area can also be found using (1/2) * base * height = (1/2) * 3 * 4 = 6, confirming Heron's formula.

Use this calculator to quickly find the perimeter and area for any valid triangle by simply inputting its three side lengths.