Triangle Area Calculator

Calculate the area of a triangle with base times height divided by two. Includes Heron's formula for three sides, a worked example, and when to use each method.

Calculate area of triangle

Formula

\\text{area} = \\frac{1}{2} \\times \\text{base} \\times \\text{height}

Worked example

Calculate the area of a triangle with base 8 cm and height 5 cm:

\\text{area} = \\frac{1}{2} \\times 8 \\times 5 = 4 \\times 5 = 20 \\text{ cm}^2

Result: 20 cm²

How to use

Enter the base length
Enter the height
Click "Calculate" to see the area

Other formulas

Heron's formula (when all three sides are known):

s = \\frac{a + b + c}{2} \\quad \\text{(semi-perimeter)}

\\text{area} = \\sqrt{s(s-a)(s-b)(s-c)}

Two sides and included angle:

\\text{area} = \\frac{1}{2} ab \\sin(C)

Triangle types

Equilateral: All sides equal, area = $\\frac{\\sqrt{3}}{4} a^2$
Isosceles: Two sides equal
Scalene: All sides different
Right-angled: One 90° angle, area = $\\frac{1}{2} \\times \\text{leg}_1 \\times \\text{leg}_2$

Common use cases

Land surveying
Roof construction
Graphics and design
Physics problems
Architecture

FAQ

Can I use the area formula for any triangle? Yes, $\\frac{1}{2} \\times \\text{base} \\times \\text{height}$ works for all triangles.

What if I don't know the height? Use Heron's formula with all three sides, or the two-sides-and-angle formula.

How do I find the height? Drop a perpendicular from the opposite vertex to the base.

Can the area be negative? No, area is always positive. If you get a negative value, check your measurements.

Is the formula the same in imperial units? Yes, the formula is unit-agnostic. Use feet, inches, or any consistent unit.

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