Triangle Area Calculator

Definition

To calculate the square meters of a triangle, you won't need a special measuring device. Square units gauge a triangle's area, the two-dimensional space inside its three sides. After measuring the triangle's sides in meters, you use a triangular area formula to determine the number of square meters in the triangle's area. One such formula is called Heron's formula, and it works for any type of triangle.

Formulas

The formula to calculate the area of a triangle using Heron's formula is:

\[ \text{Area} = \sqrt{s(s-a)(s-b)(s-c)} \]

Where:

\( s \) is the semi-perimeter of the triangle, calculated as \( s = \frac{a + b + c}{2} \).
\( a \), \( b \), and \( c \) are the lengths of the sides of the triangle.

Description

To calculate the area of a triangle using Heron's formula, you need to:

Measure all three sides of the triangle.
Add the measurements together to get the perimeter, then halve that number to determine the semi-perimeter.
Subtract each side length separately from the semi-perimeter.
Multiply the semi-perimeter by the three differences obtained in the previous step.
Calculate the square root of the product to find the area of the triangle.

Example Calculation

For a triangle with sides measuring 6 meters, 8 meters, and 10 meters:

\[ \text{Semi-perimeter} = \frac{6 + 8 + 10}{2} = 12 \, \text{meters} \] \[ \text{Area} = \sqrt{12(12-6)(12-8)(12-10)} = \sqrt{12 \times 6 \times 4 \times 2} = \sqrt{576} = 24 \, \text{square meters} \]

Triangle Area Calculator

Calculate Area Using Heron's Formula

Definition

Formulas

Description

Example Calculation