Triangle Area Formula & How to Use It

This calculator works out the area of a triangle from the base and height you enter, and it returns the area in square units. You type in the base length and the vertical height, and the calculator gives you the area instantly. The formula is one of the most used in geometry: Area = ½ × base × height.

Formula

The standard triangle area formula is written as:

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 that base to the opposite vertex (same linear units)

The height must be measured at a right angle (90°) to the base. If you use a slanted side as the height, the result will be wrong.

Worked Example

Using the default values from the calculator: base = 6 m, height = 4 m.

1. Multiply the base by the height: 6 × 4 = 24
2. Divide by 2: 24 ÷ 2 = 12

So the area is 12 m². The calculator shows 12.00 m², which matches.

When to Use This Formula

The ½ × base × height formula works for every triangle: scalene, isosceles, equilateral, acute, obtuse, and even right triangles. You only need to know one side (the base) and the perpendicular distance to the opposite corner (the height).

Common real‑life uses include:

• Calculating the area of a triangular garden bed or piece of land
• Estimating paint or flooring needed for a triangular room or wall
• Solving geometry homework or exam problems
• Working out the area of a triangular roof section for materials

If you do not have the height, you can sometimes find it using trigonometry or the Pythagorean theorem, but the base‑height formula itself is the simplest when the height is known or easy to measure.

How to Read the Result

The area is always in square units. If you measure the base and height in metres, the area is in square metres (m²). In feet, it is square feet (ft²). The number tells you how many unit squares fit inside the triangle.

For example, a triangle with base 6 m and height 4 m has an area of 12 m². That means it would take 12 square tiles of 1 m × 1 m to cover it (ignoring practical cutting issues).

If you need the area in a different unit, convert the base and height to that unit before multiplying. Do not convert the area afterwards by simply changing the label – a square metre is not the same as a square foot (1 m² = 10.7639 ft²).

Common Mistakes and Misconceptions

• Using a slanted side as the height: The height must be perpendicular to the base. For an obtuse triangle, the height may lie outside the triangle – you still measure it at a right angle to the base line.
• Forgetting to divide by 2: A triangle is half of a parallelogram with the same base and height. The most frequent error is leaving out the ½.
• Mixing units: If the base is in metres and the height in centimetres, convert one to the other first. The area unit will be the square of the unit you used for both.
• Confusing area with perimeter: Area is the space inside, perimeter is the distance around. They use different formulas.
• Using the wrong formula for special triangles: For an equilateral triangle, you can use the base‑height formula, but you must find the height first (often via the Pythagorean theorem). For a right triangle, the two legs are the base and height.

Limits of the Formula

The base‑height formula is universal, but it requires a perpendicular height. If you only know the three side lengths, you cannot directly use this formula – you would use Heron’s formula instead:

A = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2.

If you know two sides and the included angle, you can use A = ½ × a × b × sin(θ). These are alternative formulas, not different results – they all give the same area for the same triangle.

Also note that the formula assumes a flat, Euclidean triangle. On a sphere (like Earth’s surface for very large triangles), the area calculation is different.

Frequently Asked Questions

What if I only know the three side lengths?

Use Heron’s formula. First calculate the semi‑perimeter s = (a+b+c)/2, then area = √[s(s−a)(s−b)(s−c)]. This works for any triangle, but it is more tedious than base‑height when you have the height.

Can I use any side as the base?

Yes. The area is the same regardless of which side you choose as the base, as long as you use the height that is perpendicular to that side. Pick the side that is easiest to measure.

How do I find the height if it is not given?

For a right triangle, one leg is the height if the other is the base. For other triangles, you may need to draw a perpendicular line from a vertex to the opposite side and measure it, or use trigonometry if you have angles and side lengths.

Does the formula work for obtuse triangles?

Yes. The height may fall outside the triangle, but you still measure the perpendicular distance from the base line to the opposite vertex. The formula holds for all triangles.

What is the area of a triangle with base 10 cm and height 5 cm?

Using A = ½ × 10 × 5 = 25 cm². The calculator would give the same result if you entered those values.

Why do I divide by 2?

Because a triangle is exactly half of a parallelogram (or rectangle) with the same base and height. The area of a parallelogram is base × height, so the triangle is half of that.

Related

• Forest Time Lapse: Photographing a Tree & Its Surroundings
• Biometrics in Online Banking: Future & Facts
• How to Root BLU Life Pure XL: Step-by-Step Guide

in b | Base | m | 6 | 0
in h | Height | m | 4 | 0
out area | Area | m² | 0.5 * b * h | 2