Traingle Calculator

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Triangle Properties Calculator

Enter the lengths of the three sides of a triangle to calculate its perimeter, area, and determine its type.

Results:

function calculateTriangleProperties() { var sideA = parseFloat(document.getElementById('sideA').value); var sideB = parseFloat(document.getElementById('sideB').value); var sideC = parseFloat(document.getElementById('sideC').value); var perimeterResult = document.getElementById('perimeterResult'); var areaResult = document.getElementById('areaResult'); var typeResult = document.getElementById('typeResult'); var errorResult = document.getElementById('errorResult'); perimeterResult.innerHTML = "; areaResult.innerHTML = "; typeResult.innerHTML = "; errorResult.innerHTML = "; // Input validation if (isNaN(sideA) || isNaN(sideB) || isNaN(sideC) || sideA <= 0 || sideB <= 0 || sideC sideC) && (sideA + sideC > sideB) && (sideB + sideC > sideA))) { errorResult.innerHTML = 'The given side lengths do not form a valid triangle (Triangle Inequality Theorem violated).'; return; } // Calculate Perimeter var perimeter = sideA + sideB + sideC; perimeterResult.innerHTML = 'Perimeter: ' + perimeter.toFixed(2) + ' units'; // Calculate Area (Heron's Formula) var s = perimeter / 2; // Semi-perimeter var areaSquared = s * (s – sideA) * (s – sideB) * (s – sideC); if (areaSquared < 0) { // Due to floating point inaccuracies, sometimes it can be slightly negative for valid triangles areaSquared = 0; } var area = Math.sqrt(areaSquared); areaResult.innerHTML = 'Area: ' + area.toFixed(2) + ' square units'; // Determine Triangle Type var type = "; var epsilon = 1e-9; // Tolerance for floating point comparisons if (Math.abs(sideA – sideB) < epsilon && Math.abs(sideB – sideC) < epsilon) { type = 'Equilateral'; } else if (Math.abs(sideA – sideB) < epsilon || Math.abs(sideB – sideC) < epsilon || Math.abs(sideA – sideC) < epsilon) { type = 'Isosceles'; } else { type = 'Scalene'; } // Check for Right-angled triangle (Pythagorean Theorem) var sides = [sideA, sideB, sideC].sort(function(a, b){return a-b}); var aSq = sides[0] * sides[0]; var bSq = sides[1] * sides[1]; var cSq = sides[2] * sides[2]; if (Math.abs(aSq + bSq – cSq) < epsilon) { type += ' and Right-angled'; } typeResult.innerHTML = 'Triangle Type: ' + type; }

Understanding the Triangle Properties Calculator

A triangle is one of the most fundamental shapes in geometry, a polygon with three edges and three vertices. Understanding its properties like perimeter, area, and type is crucial in various fields, from architecture and engineering to art and computer graphics. Our Triangle Properties Calculator helps you quickly determine these key characteristics by simply inputting 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 are classified based on their side lengths and angles, leading to different types, each with unique properties.

Key Triangle Properties Explained

1. Perimeter

The perimeter of a triangle is the total length of its boundary. It's calculated by summing the lengths of its three sides. If the sides are 'a', 'b', and 'c', the perimeter (P) is:

P = a + b + c

The perimeter is useful for determining the amount of material needed to outline a triangular shape, such as fencing a triangular garden.

2. Area

The area of a triangle represents the amount of space it occupies in a two-dimensional plane. While the most common formula is (1/2 * base * height), when only the side lengths are known, Heron's Formula is used. If 'a', 'b', and 'c' are the side lengths, and 's' is the semi-perimeter (half of the perimeter), the area (A) is:

s = (a + b + c) / 2
A = √(s * (s - a) * (s - b) * (s - c))

The area is essential for calculating the surface coverage, like the amount of paint needed for a triangular wall or the size of a triangular plot of land.

3. Triangle Type

Triangles are classified based on their side lengths:

  • Equilateral Triangle: All three sides are equal in length. All three angles are also equal (60 degrees each).
  • Isosceles Triangle: At least two sides are equal in length. The angles opposite the equal sides are also equal.
  • Scalene Triangle: All three sides have different lengths. All three angles are also different.

Additionally, triangles can be classified by their angles, with the most common being:

  • Right-angled Triangle: One of its angles is exactly 90 degrees. The side opposite the right angle is called the hypotenuse, and its length relates to the other two sides (legs) by the Pythagorean Theorem: a² + b² = c².

How to Use the Calculator

  1. Enter Side Lengths: Input the numerical values for the lengths of Side A, Side B, and Side C into the respective fields. Ensure these are positive numbers.
  2. Click "Calculate Properties": Press the button to initiate the calculation.
  3. View Results: The calculator will display the calculated perimeter, area, and the type of triangle (e.g., "Scalene and Right-angled").
  4. Error Handling: If the entered side lengths cannot form a valid triangle (e.g., 1, 2, 10, which violates the triangle inequality theorem), an error message will be displayed.

Example Calculation

Let's consider a common example: a right-angled triangle with sides 3, 4, and 5 units.

  • Side A: 3
  • Side B: 4
  • Side C: 5

Using the calculator:

  • Perimeter: 3 + 4 + 5 = 12 units
  • Semi-perimeter (s): 12 / 2 = 6
  • Area: √(6 * (6 – 3) * (6 – 4) * (6 – 5)) = √(6 * 3 * 2 * 1) = √36 = 6 square units
  • Triangle Type: Since 3² + 4² = 9 + 16 = 25, and 5² = 25, it's a Right-angled triangle. As all sides are different, it's also Scalene. So, the type is "Scalene and Right-angled".

This calculator simplifies complex geometric calculations, making it an invaluable tool for students, educators, and professionals alike.

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