Area of a Triangle: Formula, Examples & Calculator

This calculator works out the area of a triangle from the base and height you enter, and returns the result in square units. Enter the base length and the perpendicular height, and you get the area instantly, with the formula and a worked example shown below. The area of a triangle is always half the area of a rectangle with the same base and height.

Formula

The standard formula for the area of a triangle is:

Area = ½ × base × height

In symbols: A = ½ × b × h

• A = area of the triangle (square units, e.g., m², cm², ft²)
• b = length of the base (any side you choose as the base, in linear units)
• h = perpendicular height from the base to the opposite vertex (same linear units)

The height must be measured at a right angle to the base, not along the slanted side. This formula works for any triangle—right, acute, obtuse, scalene, isosceles, or equilateral—as long as you know a base and its corresponding height.

Worked Example

Using the calculator defaults: base = 10 m, height = 6 m.

1. Write the formula: A = ½ × b × h
2. Plug in the values: A = ½ × 10 × 6
3. Multiply 10 × 6 = 60
4. Take half: 60 ÷ 2 = 30

The area is 30 m². The calculator gives the same result: 30.00 m².

Why the Half Appears

A triangle is exactly half of a rectangle (or parallelogram) with the same base and height. If you draw a diagonal across a rectangle, you get two congruent right triangles, each with half the rectangle’s area. For non-right triangles, you can visualize the same by slicing and rearranging—the triangle always occupies half of the bounding rectangle. That geometric fact is why the formula is ½ × base × height, not base × height.

Other Ways to Find the Area

The base-height formula is the most common, but sometimes you don’t have the height. Here are other valid methods:

• Heron’s formula: when you know all three sides. Compute semi-perimeter s = (a+b+c)/2, then area = √[s(s−a)(s−b)(s−c)].
• Two sides and the included angle: area = ½ × a × b × sin(C), where C is the angle between sides a and b.
• Equilateral triangle: area = (√3/4) × side².
• Coordinates: if you know the vertices (xâ‚�,yâ‚�), (xâ‚‚,yâ‚‚), (x₃,y₃), use the shoelace formula: area = ½ |xâ‚�(y₂−y₃) + xâ‚‚(y₃−yâ‚�) + x₃(yâ‚�−yâ‚‚)|.

Common Mistakes and How to Avoid Them

• Using a slanted side as the height: the height must be perpendicular to the base. In an obtuse triangle, the height may lie outside the triangle—that’s fine, the formula still works.
• Mixing units: if base is in meters and height in centimeters, convert one first. The area will be in square units of the consistent unit.
• Forgetting to halve: the most frequent error is using base × height without the ½. Always divide by 2.
• Assuming the formula only works for right triangles: it works for all triangles.

Real-World Uses

Triangle area shows up in many practical places:

• Roofing and construction: gable ends are triangles; you need their area for materials.
• Land surveying: irregular plots are often split into triangles for area calculation.
• Fabric and sewing: triangular pieces for quilts or flags.
• Geometry homework: the formula is a building block for more complex shapes.

For any polygon, you can break it into triangles and sum their areas—this is why the triangle is the basic unit of area measurement.

Frequently Asked Questions

What if the triangle is not right-angled?

The formula A = ½ × base × height works for every triangle. The height is the perpendicular distance from the base to the opposite vertex, not the length of a slanted side. For an obtuse triangle, the height may fall outside the triangle, but the measurement is still taken perpendicular to the base.

How do I find the area if I only know the three sides?

Use Heron’s formula: first calculate the semi-perimeter s = (a+b+c)/2, then area = √[s(s−a)(s−b)(s−c)]. For example, sides 3, 4, 5: s=6, area = √[6×3×2×1] = √36 = 6 square units.

Can I use any side as the base?

Yes. Choose any side as the base, then measure the height perpendicular to that side from the opposite vertex. The area will be the same no matter which side you pick, as long as you use the corresponding height.

What is the area of an equilateral triangle with side length 6 cm?

Use the special formula: area = (√3/4) × side² = (1.732/4) × 36 ≈ 15.59 cm². You can also find the height (5.196 cm) and use the base-height formula.

How do I convert area to different units?

If you measure in meters, area is in square meters. To convert to square feet, multiply by 10.764 (since 1 m = 3.28084 ft, so 1 m² = 10.7639 ft²). For square centimeters, multiply square meters by 10,000. Always convert the linear measurements to the same unit first.

Does the formula work for triangles drawn on a curved surface?

No. This formula is for flat (Euclidean) triangles. On a sphere, the area depends on the angles and the radius of the sphere, and the sum of angles exceeds 180°. For everyday practical purposes on the Earth’s surface, the flat formula is accurate for small areas.

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in b | Base | m | 10 | 0
in h | Height | m | 6 | 0
out area | Area | m² | 0.5 * b * h | 2