Geometry Triangle Calculator

Triangle Geometry Calculator

Area (Base & Height) Area & Perimeter (Three Sides)

Calculate Area using Base and Height

Calculate Area & Perimeter using Three Sides

Results will appear here.

function toggleInputFields() { var mode = document.getElementById('calculationMode').value; if (mode === 'baseHeight') { document.getElementById('baseHeightInputs').style.display = 'block'; document.getElementById('threeSidesInputs').style.display = 'none'; } else { document.getElementById('baseHeightInputs').style.display = 'none'; document.getElementById('threeSidesInputs').style.display = 'block'; } document.getElementById('resultOutput').innerHTML = 'Results will appear here.'; } function calculateTriangle() { var mode = document.getElementById('calculationMode').value; var resultDiv = document.getElementById('resultOutput'); resultDiv.style.color = '#333'; // Reset color for new results resultDiv.style.backgroundColor = '#e9f7ef'; // Reset background for new results var outputHTML = "; if (mode === 'baseHeight') { var base = parseFloat(document.getElementById('triangleBase').value); var height = parseFloat(document.getElementById('triangleHeight').value); if (isNaN(base) || isNaN(height) || base <= 0 || height <= 0) { resultDiv.innerHTML = 'Please enter valid positive numbers for Base and Height.'; resultDiv.style.backgroundColor = '#f8d7da'; return; } var area = 0.5 * base * height; outputHTML = 'Area: ' + area.toFixed(2) + ' square units'; outputHTML += '(Perimeter cannot be determined with only base and height without additional information.)'; } else if (mode === 'threeSides') { var sideA = parseFloat(document.getElementById('sideA').value); var sideB = parseFloat(document.getElementById('sideB').value); var sideC = parseFloat(document.getElementById('sideC').value); 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 violated).'; resultDiv.style.backgroundColor = '#f8d7da'; return; } var perimeter = sideA + sideB + sideC; var s = perimeter / 2; // Semi-perimeter for Heron's formula var area = Math.sqrt(s * (s – sideA) * (s – sideB) * (s – sideC)); outputHTML = 'Perimeter: ' + perimeter.toFixed(2) + ' units'; outputHTML += 'Area: ' + area.toFixed(2) + ' square units'; } resultDiv.innerHTML = outputHTML; } // Initialize the correct input fields on page load window.onload = toggleInputFields;

Understanding Triangle Geometry: Area and Perimeter

Triangles are fundamental shapes in geometry, forming the basis for many complex structures and calculations. Understanding how to calculate their area and perimeter is crucial in various fields, from construction and engineering to art and design. This calculator helps you quickly determine these key properties based on the information you have.

What is a Triangle?

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. The sum of the internal angles of a triangle in Euclidean geometry is always 180 degrees.

Calculating the Area of a Triangle

The area of a triangle represents the amount of two-dimensional space it occupies. There are several ways to calculate the area, depending on the information available:

1. Using Base and Height

The most common formula for the area of a triangle involves its base and height. The 'base' can be any side of the triangle, and the 'height' (or altitude) is the perpendicular distance from the opposite vertex to that base.

Formula: Area = (1/2) × Base × Height

Example: If a triangle has a base of 10 units and a height of 5 units:

• Base = 10
• Height = 5
• Area = (1/2) × 10 × 5 = 25 square units

This method is straightforward when the perpendicular height is known or can be easily measured.

2. Using Three Sides (Heron's Formula)

When you know the lengths of all three sides of a triangle (Side A, Side B, and Side C), you can use Heron's Formula to find its area. This is particularly useful when the height is not readily available.

Formula: Area = √[s(s – A)(s – B)(s – C)]

Where 's' is the semi-perimeter of the triangle, calculated as: s = (A + B + C) / 2

Example: Consider a triangle with sides A=3, B=4, and C=5 units (a right-angled triangle):

• Side A = 3
• Side B = 4
• Side C = 5
• Semi-perimeter (s) = (3 + 4 + 5) / 2 = 12 / 2 = 6
• Area = √[6 × (6 – 3) × (6 – 4) × (6 – 5)]
• Area = √[6 × 3 × 2 × 1] = √36 = 6 square units

Before applying Heron's formula, it's important to ensure that the three sides can actually form a triangle. This is checked using the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side (e.g., A + B > C, A + C > B, and B + C > A).

Calculating the Perimeter of a Triangle

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: Using the same triangle with sides A=3, B=4, and C=5 units:

• Side A = 3
• Side B = 4
• Side C = 5
• Perimeter = 3 + 4 + 5 = 12 units

The perimeter can only be calculated if all three side lengths are known. If you only have the base and height, you cannot determine the perimeter without additional information (like angles or other side lengths).

Using the Calculator

Our Triangle Geometry Calculator provides two modes:

1. Area (Base & Height): Input the length of the base and the corresponding perpendicular height to get the area.
2. Area & Perimeter (Three Sides): Input the lengths of all three sides (A, B, and C) to calculate both the area (using Heron's formula) and the perimeter. The calculator will also validate if the given sides can form a real triangle.

Simply select your desired calculation mode, enter the required positive numerical values, and click "Calculate Triangle Properties" to see the results.