Area of Triangle Calculator with 3 Sides

Area of a Triangle Calculator (3 Sides)

Side A Length:

Side B Length:

Side C Length:

Understanding the Area of a Triangle with Three Sides

Calculating the area of a triangle is a fundamental concept in geometry. While the most common formula involves the base and height (Area = 0.5 * base * height), this isn't always practical if you only know the lengths of the three sides. This is where Heron's Formula becomes incredibly useful.

What is Heron's Formula?

Heron's Formula, named after Heron of Alexandria, provides a way to calculate the area of a triangle when the lengths of all three sides are known. It's particularly handy when you don't have information about the triangle's height or angles.

How Heron's Formula Works

The formula involves two main steps:

Calculate the Semi-Perimeter (s): The semi-perimeter is half the perimeter of the triangle. If the sides are 'a', 'b', and 'c', then:
s = (a + b + c) / 2
Apply Heron's Formula: Once you have the semi-perimeter, the area (A) is calculated as:
A = √(s * (s - a) * (s - b) * (s - c))

It's important to note that for a valid triangle to exist, the sum of the lengths of any two sides must be greater than the length of the third side (Triangle Inequality Theorem). Our calculator checks for this condition.

How to Use This Calculator

Our Area of a Triangle Calculator makes it easy to find the area using Heron's Formula:

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 Area": The calculator will instantly compute and display the area of the triangle, or an error message if the side lengths do not form a valid triangle.

Example Calculation

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

Side A = 7 units
Side B = 8 units
Side C = 9 units

Here's how Heron's Formula would be applied:

Calculate Semi-Perimeter (s):
s = (7 + 8 + 9) / 2 = 24 / 2 = 12
Calculate Area (A):
A = √(12 * (12 - 7) * (12 - 8) * (12 - 9))
A = √(12 * 5 * 4 * 3)
A = √(720)
A ≈ 26.83 square units

Using the calculator with these values will yield the same result, making complex calculations simple and quick.

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