Area Calculator Triangle: How to Find It Fast

This calculator finds the area of a triangle from its base and height. You enter the base length and the height (the perpendicular distance from the base to the opposite vertex), and it returns the area in square units. The formula used is the standard one: Area = ½ × base × height.

Formula

The area of a triangle is given by:

Area = ½ × base × height

In symbols: A = ½ × b × h

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

The height must be measured at a right angle to the base. It is not the length of a slanted side.

Worked Example

Using the default values from the calculator: base = 10 m, height = 5 m.

1. Write the formula: A = ½ × b × h
2. Plug in the numbers: A = ½ × 10 × 5
3. Multiply base and height: 10 × 5 = 50
4. Multiply by ½ (or divide by 2): 50 ÷ 2 = 25

The area is 25 m². The calculator shows 25.00 m², which is the same result rounded to two decimals.

When to Use This Calculator

Use this tool whenever you know the base and the perpendicular height of a triangle. Common situations include:

• Finding the area of a triangular plot of land (if you can measure the base and height)
• Calculating the amount of material needed for a triangular sail, banner, or roof section
• Solving geometry homework problems that give base and height
• Estimating the area of a triangular garden bed to buy soil or mulch

If you do not know the height, you cannot use this simple formula directly. You would need another method, such as Heron’s formula (if you know all three sides) or trigonometry (if you know two sides and the included angle).

How to Read the Result

The result is in square units of whatever you used for the base and height. For example:

• Base in meters and height in meters → area in square meters (m²)
• Base in feet and height in feet → area in square feet (ft²)
• Base in centimeters and height in centimeters → area in square centimeters (cm²)

If you need a different unit, convert the base and height to that unit before calculating. Do not convert the area after the fact unless you know the conversion factor for square units (e.g., 1 m² = 10.7639 ft²).

Common Mistakes and Misconceptions

• Using a slanted side as the height. The height must be perpendicular to the base. In a non-right triangle, the height is often inside the triangle, but it can also be outside if the triangle is obtuse. Always measure the vertical distance from the base line to the opposite vertex.
• Unit mismatch. If the base is in meters and the height is in centimeters, the area will be wrong. Convert one to the other first.
• Forgetting the ½. The area of a triangle is half the area of a rectangle with the same base and height. Omitting the ½ doubles your answer.
• Thinking the formula works for any three sides. It only works with a base and its corresponding height. If you only know the side lengths, use Heron’s formula instead.

Limits of the Formula

This formula works for any triangle—right, acute, or obtuse—as long as you correctly identify the base and the perpendicular height. It does not work if the height is not perpendicular. For triangles where the height is not easy to measure, other formulas are more practical:

• Heron’s formula: Use when you know all three sides. Area = √(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2.
• Trigonometric formula: Area = ½ × a × b × sin(C), where a and b are two sides and C is the included angle.
• Coordinate formula: If you know the vertices’ coordinates, use the shoelace formula.

Frequently Asked Questions

Can I use this calculator for a right triangle?

Yes. For a right triangle, the two legs are perpendicular, so you can use one leg as the base and the other as the height. The formula works exactly the same.

What if I only know the three side lengths?

Use Heron’s formula: first compute the semi-perimeter s = (a+b+c)/2, then area = √(s(s-a)(s-b)(s-c)). This calculator does not do that, but you can find a dedicated Heron’s formula calculator elsewhere on this site.

What if the triangle is obtuse and the height falls outside?

The formula still works. Extend the base line and measure the perpendicular distance from the extension to the opposite vertex. That distance is the height. The area is still ½ × base × height.

How do I convert the area to different units?

Convert the base and height to the target unit before multiplying. For example, to get square feet from meters, multiply both base and height by 3.28084, then compute the area. Alternatively, convert the area directly using square-unit conversion factors (e.g., 1 m² = 10.7639 ft²).

Why is the area half of base times height?

A triangle is exactly half of a rectangle 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 any triangle, you can construct a rectangle around it, and the triangle occupies half of that rectangle.

Can I use this for a 3D triangle?

No. A triangle is a 2D shape. If you mean a triangular prism or pyramid, you need volume formulas, not area. The surface area of a 3D shape would involve the areas of its faces, which you can calculate using this formula for each triangular face.

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in b | Base | m | 10 | 0
in h | Height | m | 5 | 0
out area | Area | m² | 0.5 * b * h | 2