Triangle Area Calculator
Calculation Method
Formulas
• Base & Height: A = ½ × b × h
• Heron's: A = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2
• Two Sides & Angle: A = ½ × a × b × sin(C)
Find the area of a triangle three ways: from a base and its perpendicular height, from the three side lengths with Heron's formula, or from two sides and the angle between them.
Formula
Worked Example
The semi-perimeter is s = (5 + 6 + 7) ÷ 2 = 9, so A = √(9 × 4 × 3 × 2) = √216 ≈ 14.70. No height or angle is needed.
Frequently Asked Questions
Which height goes into the base × height formula?
The perpendicular distance from the base to the opposite corner. In an obtuse triangle it can fall outside the triangle, on the extension of the base. The length of a slanted side is not the height.
When should I use Heron's formula?
When you know all three sides but no height or angle, as when a plot of land is measured with a tape. The sides must satisfy the triangle inequality: each one shorter than the other two combined.
How do I find the area from two sides and an angle?
Use A = ½ × a × b × sin C, where C is the angle between sides a and b. For a = 8, b = 10 and C = 30°: ½ × 8 × 10 × 0.5 = 20.