Area of a Triangle Calculator
Calculate the area of a triangle using base and height, or all three sides (Heron's formula). See also Area of Rectangle Calculator and Area of Trapezoid Calculator.
How to Calculate the Area of a Triangle
The most common method is to multiply the base by the height and divide by 2: A = ½ × base × height. The height must be perpendicular to the base. If you know all three side lengths instead, use Heron's formula: first find the semi-perimeter s = (a + b + c) / 2, then A = √(s(s−a)(s−b)(s−c)). Both methods give the same result for the same triangle.
Triangle Area Formulas
A = ½ × base × height
Heron's formula:
s = (a + b + c) / 2
A = √(s × (s − a) × (s − b) × (s − c))
Example
Find the area of a triangle with base 10 and height 8:
A = ½ × base × height
A = ½ × 10 × 8
A = 40 square units
Using Heron's formula with sides 5, 6, 7:
s = (5 + 6 + 7) / 2 = 9
A = √(9 × 4 × 3 × 2) = √216
A ≈ 14.6969 square units
Triangle Area Reference Table
| Base | Height | Area |
|---|---|---|
| 3 | 2 | 3.00 |
| 4 | 3 | 6.00 |
| 5 | 4 | 10.00 |
| 6 | 5 | 15.00 |
| 8 | 6 | 24.00 |
| 10 | 8 | 40.00 |
| 12 | 9 | 54.00 |
| 15 | 10 | 75.00 |
| 20 | 12 | 120.00 |
| 25 | 15 | 187.50 |
| 50 | 30 | 750.00 |
| 100 | 60 | 3000.00 |
Frequently Asked Questions
What is Heron's formula?
Heron's formula calculates the area of a triangle when you know all three side lengths. First compute the semi-perimeter s = (a+b+c)/2, then A = √(s(s−a)(s−b)(s−c)). It works for any triangle.
Does the height have to be inside the triangle?
Not necessarily. For obtuse triangles, the height from the longest side falls outside the triangle. The formula A = ½bh still works — the height is the perpendicular distance from the base line to the opposite vertex.
How do I know if three sides form a valid triangle?
Three sides form a valid triangle if and only if the sum of any two sides is greater than the third side. This is called the triangle inequality theorem.
What is the area of an equilateral triangle?
For an equilateral triangle with side length s, the area is A = (√3/4) × s². For example, a triangle with side 6 has area = (√3/4) × 36 ≈ 15.588.