Area of Triangle Calculator
Area (Base×Height)
—
Area (Heron's Formula)
—
Perimeter (from sides)
—
How to Calculate the Area of a Triangle
The most common method to find a triangle's area is the base-height formula: A = ½ × base × height. The height must be perpendicular to the base. This method works for any triangle as long as you know the base length and the corresponding height.
When you know all three sides but not the height, use Heron's formula. First calculate the semi-perimeter: s = (a + b + c) / 2. Then: A = √[s(s-a)(s-b)(s-c)]. This elegant formula dates back to the 1st century CE and works for any valid triangle.
Remember that three sides form a valid triangle only if the sum of any two sides is greater than the third side (triangle inequality theorem). This calculator checks for validity and alerts you if the sides cannot form a triangle.
Frequently Asked Questions
What is the easiest way to find the area of a triangle?
The simplest formula is A = ½ × base × height. Multiply the base by the perpendicular height and divide by 2.
What is Heron's formula?
Heron's formula calculates triangle area from all three sides: A = √[s(s-a)(s-b)(s-c)] where s is the semi-perimeter (a+b+c)/2.
How do I find the height of a triangle if I know the area?
Rearrange the formula: height = 2 × Area / base. This gives the perpendicular height corresponding to the base you used.
Can a triangle have sides 1, 2, and 5?
No. For three lengths to form a valid triangle, the sum of any two sides must exceed the third. Since 1 + 2 = 3 < 5, these cannot form a triangle.