Triangle Area Calculator
Find the area of any triangle using three different methods.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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This calculator supports three methods for finding the area of a triangle. Choose the one that matches the information you have.
- Select a method. Choose "Base and Height" if you know the base and perpendicular height. Choose "Heron's Formula" if you know all three side lengths. Choose "SAS" if you know two sides and the angle between them.
- Enter the values. The input fields change based on your selected method. Fill in all required measurements.
- Read the result. The area displays instantly with the formula used. Copy or share the result with the action buttons.
The base-height method uses A = 0.5 * base * height. Heron's formula uses the semi-perimeter: s = (a+b+c)/2, then A = sqrt(s(s-a)(s-b)(s-c)). The SAS method uses A = 0.5 * a * b * sin(C). All three methods give the same answer when applied to the same triangle.
About Triangle Area Formulas
The base-height formula (A = 1/2 * b * h) is the simplest and most commonly taught method. It requires knowing the perpendicular height, which is not always easy to measure directly. Heron's formula is useful when you only know the three side lengths, as it avoids the need for height. It was attributed to Hero of Alexandria around 60 AD, though it may have been known earlier. The SAS (side-angle-side) formula uses trigonometry and is particularly useful in surveying and navigation where angles are measured with instruments. Each method has its best use case depending on what measurements are available.
Frequently Asked Questions
What is Heron's formula?
Heron's formula calculates triangle area from three side lengths. First find the semi-perimeter s = (a+b+c)/2, then the area is sqrt(s * (s-a) * (s-b) * (s-c)). For a 3-4-5 triangle, s = 6, area = sqrt(6*3*2*1) = 6.
When should I use the SAS method?
Use the SAS method when you know two side lengths and the angle between them (the included angle). The formula is A = 0.5 * a * b * sin(C). This is common in surveying, where distances and angles are measured with instruments.
Can three side lengths form a valid triangle?
Three sides form a valid triangle only if the sum of any two sides is greater than the third side. This is called the triangle inequality. If this condition is not met, the calculator will not show a result because no such triangle exists.