Calculator for Triangles

Triangle Properties Calculator

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

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function calculateTriangleProperties() { 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('triangleResult'); // Input validation 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 areaSquared = s * (s – sideA) * (s – sideB) * (s – sideC); // Due to floating point inaccuracies, areaSquared might be slightly negative for valid triangles. // Clamp it to 0 if it's very close to 0. var area = (areaSquared -1e-9) ? 0 : Math.sqrt(areaSquared); // Determine Triangle Type var triangleType = "; var epsilon = 0.0001; // Tolerance for floating point comparisons // Classify by side lengths if (Math.abs(sideA – sideB) < epsilon && Math.abs(sideB – sideC) < epsilon) { triangleType = 'Equilateral'; } else if (Math.abs(sideA – sideB) < epsilon || Math.abs(sideB – sideC) < epsilon || Math.abs(sideA – sideC) < epsilon) { triangleType = 'Isosceles'; } else { triangleType = 'Scalene'; } // Classify by angles (Acute, Right, Obtuse) // Sort sides to easily identify the longest side (potential hypotenuse) var sides = [sideA, sideB, sideC].sort(function(a, b){return a-b}); var a_sq = sides[0] * sides[0]; var b_sq = sides[1] * sides[1]; var c_sq = sides[2] * sides[2]; // Longest side if (Math.abs(a_sq + b_sq – c_sq) < epsilon) { triangleType += ' and Right-angled'; } else if (a_sq + b_sq < c_sq) { triangleType += ' and Obtuse'; } else { triangleType += ' and Acute'; } // Display results var resultsHTML = '

Calculation Results:

'; resultsHTML += 'Perimeter: ' + perimeter.toFixed(2) + ' units'; resultsHTML += 'Area: ' + area.toFixed(2) + ' square units'; resultsHTML += 'Triangle Type: ' + triangleType + "; resultDiv.innerHTML = resultsHTML; } .triangle-calculator-container { font-family: Arial, sans-serif; background-color: #f9f9f9; padding: 20px; border-radius: 8px; max-width: 600px; margin: 20px auto; box-shadow: 0 2px 4px rgba(0, 0, 0, 0.1); } .triangle-calculator-container h2 { color: #333; text-align: center; margin-bottom: 20px; } .triangle-calculator-container p { color: #555; line-height: 1.6; } .calculator-input-group { margin-bottom: 15px; } .calculator-input-group label { display: block; margin-bottom: 5px; font-weight: bold; color: #444; } .calculator-input-group input[type="number"] { width: calc(100% – 80px); /* Adjust width for 'units' text */ padding: 10px; border: 1px solid #ddd; border-radius: 4px; box-sizing: border-box; margin-right: 5px; } .triangle-calculator-container button { background-color: #007bff; color: white; padding: 12px 20px; border: none; border-radius: 4px; cursor: pointer; font-size: 16px; width: 100%; margin-top: 10px; } .triangle-calculator-container button:hover { background-color: #0056b3; } .calculator-result { margin-top: 25px; padding: 15px; background-color: #e9f7ef; border: 1px solid #d4edda; border-radius: 4px; color: #155724; } .calculator-result h3 { color: #155724; margin-top: 0; } .calculator-result p { margin-bottom: 5px; } .calculator-result .error { color: #721c24; background-color: #f8d7da; border-color: #f5c6cb; padding: 10px; border-radius: 4px; }

Understanding Triangles and Their Properties

A triangle is one of the most fundamental shapes in geometry, defined as a polygon with three edges and three vertices. It's a closed, two-dimensional figure that forms the basis for many complex structures and mathematical concepts. Understanding the properties of triangles is crucial in fields ranging from architecture and engineering to computer graphics and physics.

Key Properties of Triangles

• Sides: Every triangle has three sides, which are line segments connecting its vertices.
• Angles: Every triangle has three interior angles. The sum of these interior angles always equals 180 degrees.
• Vertices: These are the points where the sides of the triangle meet.

Types of Triangles by Side Lengths

Triangles can be classified based on the lengths of their sides:

• Equilateral Triangle: All three sides are equal in length. Consequently, all three interior angles are also equal, each measuring 60 degrees.
• 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. As a result, all three interior angles are also different.

Types of Triangles by Angles

Triangles can also be classified based on the measure of their largest interior angle:

• Acute Triangle: All three interior angles are acute (less than 90 degrees).
• Right-angled Triangle: One of the interior angles is exactly 90 degrees (a right angle). The side opposite the right angle is called the hypotenuse, and it is always the longest side.
• Obtuse Triangle: One of the interior angles is obtuse (greater than 90 degrees).

The Triangle Inequality Theorem

A fundamental rule for any valid triangle 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. If this condition is not met, the three side lengths cannot form a closed triangle.

For sides a, b, and c:

• a + b > c
• a + c > b
• b + c > a

Calculating Perimeter

The perimeter of a triangle is the total length of its boundary. It is simply the sum of the lengths of its three sides.

Formula: Perimeter = Side A + Side B + Side C

Example: If a triangle has sides of 3 units, 4 units, and 5 units, its perimeter is 3 + 4 + 5 = 12 units.

Calculating Area (Heron's Formula)

The area of a triangle is the amount of two-dimensional space it occupies. While the most common formula is (1/2) * base * height, this requires knowing the height, which isn't always readily available. When you know the lengths of all three sides, Heron's Formula is incredibly useful.

Heron's Formula Steps:

1. First, calculate the semi-perimeter (s), which is half of the perimeter: s = (Side A + Side B + Side C) / 2
2. Then, use the semi-perimeter in the area formula: Area = √(s * (s - Side A) * (s - Side B) * (s - Side C))

Example: For a triangle with sides 3, 4, and 5 units:

• Semi-perimeter (s) = (3 + 4 + 5) / 2 = 12 / 2 = 6 units
• Area = √(6 * (6 – 3) * (6 – 4) * (6 – 5))
• Area = √(6 * 3 * 2 * 1)
• Area = √(36)
• Area = 6 square units

This example also happens to be a right-angled triangle, where the area can also be calculated as (1/2) * base * height = (1/2) * 3 * 4 = 6 square units, confirming Heron's formula.

How to Use the Calculator

Our Triangle Properties Calculator simplifies these calculations for you. Simply enter the lengths of the three sides of your triangle into the respective fields. Click the "Calculate Properties" button, and the calculator will instantly display the triangle's perimeter, its area, and classify its type (e.g., Scalene and Right-angled, Equilateral and Acute).

Remember to ensure your side lengths adhere to the Triangle Inequality Theorem for a valid result.