Calculate a Triangle – Loan calculator

Triangle Calculator

Side A Length:

Side B Length:

Side C Length:

Results:

Enter side lengths and click 'Calculate Triangle' to see results.

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("triangleResult"); 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 cannot form a valid triangle. The sum of any two sides must be greater than the third side."; 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 = "Perimeter: " + perimeter.toFixed(2) + " units" + "Area: " + area.toFixed(2) + " square units"; }

Understanding the Triangle Calculator

A triangle is one of the most fundamental shapes in geometry, a polygon with three edges and three vertices. It's a cornerstone of mathematics, engineering, and architecture. Our Triangle Calculator helps you quickly determine two key properties of any triangle: its perimeter and its area, simply by knowing the lengths of its three sides.

How to Use the Calculator

Using the calculator is straightforward:

Enter Side A Length: Input the length of the first side of your triangle.
Enter Side B Length: Input the length of the second side.
Enter Side C Length: Input the length of the third side.
Click "Calculate Triangle": The calculator will instantly display the perimeter and area of the triangle formed by these sides.

Remember to use consistent units for all side lengths (e.g., all in centimeters, all in meters, all in inches). The resulting perimeter will be in the same unit, and the area will be in square units (e.g., square centimeters, square meters, square inches).

The Math Behind the Calculator

1. Perimeter Calculation

The perimeter of any polygon is simply the sum of the lengths of its sides. For a triangle with sides A, B, and C, the perimeter (P) is calculated as:

P = A + B + C

This is a direct and simple calculation, representing the total distance around the triangle.

2. Area Calculation (Heron's Formula)

When you know the lengths of all three sides of a triangle, you can calculate its area using Heron's Formula. This formula is particularly useful because it doesn't require knowing the height or any angles of the triangle.

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

s = (A + B + C) / 2

Then, the area (Area) is calculated using the following formula:

Area = √(s * (s - A) * (s - B) * (s - C))

This formula ensures an accurate area calculation for any valid triangle.

3. 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. Our calculator checks for this condition:

A + B > C
A + C > B
B + C > A

If these conditions are not met, the given side lengths cannot form a real triangle, and the calculator will inform you of this impossibility.

Examples of Triangle Calculations

Example 1: A Right-Angled Triangle

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

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

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

(Inputting 3, 4, and 5 into the calculator will yield these results.)

Example 2: An Equilateral Triangle

An equilateral triangle has all three sides equal. Let's use sides of 7 units each.

Side A = 7
Side B = 7
Side C = 7

Perimeter: 7 + 7 + 7 = 21 units

Semi-perimeter (s): 21 / 2 = 10.5

Area: √(10.5 * (10.5 – 7) * (10.5 – 7) * (10.5 – 7)) = √(10.5 * 3.5 * 3.5 * 3.5) = √(10.5 * 42.875) = √450.1875 ≈ 21.22 square units

(Inputting 7, 7, and 7 into the calculator will yield these results.)

This calculator is a handy tool for students, engineers, designers, or anyone needing quick and accurate triangle property calculations based on side lengths.