Area of Triangle Calculator

Formula

The formula to calculate the Area of a Triangle is:

\[ \text{Area} = \sqrt{(\text{Side A} + \text{Side B} + \text{Side C}) \cdot (\text{Side B} + \text{Side C} - \text{Side A}) \cdot (\text{Side A} - \text{Side B} + \text{Side C}) \cdot (\text{Side A} + \text{Side B} - \text{Side C})} \div 4 \]

Where:

\(\text{Area}\) is the amount of region or space occupied by the triangle (square meters)
\(\text{Side A}\) is the length of side A of the triangle (meters)
\(\text{Side B}\) is the length of side B of the triangle (meters)
\(\text{Side C}\) is the length of side C of the triangle (meters)

Area of Triangle Definition

The Area of Triangle is the amount of region or space occupied by the triangle.

Example Calculation

Let's assume the following values:

Side A = 10 m
Side B = 14 m
Side C = 20 m

Using the formula:

\[ \text{Area} = \sqrt{(10 + 14 + 20) \cdot (14 + 20 - 10) \cdot (10 - 14 + 20) \cdot (10 + 14 - 20)} \div 4 \]

Evaluating:

\[ \text{Area} = \sqrt{44 \cdot 24 \cdot 16 \cdot 4} \div 4 \]

\[ \text{Area} = \sqrt{67584} \div 4 \]

\[ \text{Area} = 259.9923072370877 \div 4 \]

\[ \text{Area} = 64.9923072370877 \]

The Area of the Triangle is 64.9923072370877 square meters.

Area of Triangle Conversion Table

Side A (m)	Side B (m)	Side C (m)	Area (square meters)
5	10	15	0.000000000000
5	10	20	nan
5	10	25	nan
5	15	15	36.975498644373
5	15	20	0.000000000000
5	15	25	nan
5	20	15	0.000000000000
5	20	20	49.607837082461
5	20	25	0.000000000000
10	10	15	49.607837082461
10	10	20	0.000000000000
10	10	25	nan
10	15	15	70.710678118655
10	15	20	72.618437741389
10	15	25	0.000000000000
10	20	15	72.618437741389
10	20	20	96.824583655185
10	20	25	94.991775959817
15	10	15	70.710678118655
15	10	20	72.618437741389
15	10	25	0.000000000000
15	15	15	97.427857925749
15	15	20	111.803398874989
15	15	25	103.644524698606
15	20	15	111.803398874989
15	20	20	139.053721633044
15	20	25	150.000000000000