Triangle Area Calculator: Base & Height Method

This calculator works out the area of a triangle when you know its base and perpendicular height. Enter the base length and the height measured at a right angle to that base, and you get the area in square units. The formula used is the standard one taught at Key Stage 2: area = ½ × base × height.

Formula

The area of a triangle is calculated with the simple formula:

Area = ½ × base × height

In symbols: A = ½ × b × h

• A = area (square units, e.g. cm², m², in²)
• b = base length (units of length, e.g. cm, m, in)
• h = perpendicular height (same units as base)

The height must be measured at a right angle (90°) to the base, not along the slanted side. This is the most common mistake students make.

Worked Example

Using the default values from the calculator above (base = 8 cm, height = 5 cm):

1. Multiply the base by the height: 8 × 5 = 40
2. Halve the result: 40 ÷ 2 = 20

The area is 20 cm². The calculator shows 20.00 cm², which is the same answer rounded to two decimal places.

When to Use This Formula

This formula works for every triangle, no matter its shape: right-angled, equilateral, isosceles, or scalene. The only requirement is that you know a base and its corresponding perpendicular height. In KS2 (ages 7–11 in the UK), this is the main method taught. Children usually meet it in Year 6, often with shapes drawn on squared paper or with measurements given directly.

Real-life uses include finding the area of a triangular garden, a sail, a roof section, or a piece of fabric. Builders, designers, and tailors use it regularly.

How to Choose the Base and Height

Any side can be the base. The height is the perpendicular distance from that base to the opposite vertex (the corner point). You can rotate the triangle and still use the same rule.

• If the triangle is right-angled, the two shorter sides are the base and height.
• If the triangle is drawn on a grid, count squares for the base and the vertical height.
• If only the side lengths are given (e.g. 3 cm, 4 cm, 5 cm), you cannot use this formula unless you also know one height. For that, you need Heron’s formula, which is beyond KS2.

Common Mistakes and Misconceptions

• Using a slanted side as the height. The height must be perpendicular (at 90°) to the base. In a non-right triangle, the height is often inside the shape, but it can be outside for obtuse triangles.
• Forgetting to halve. The most frequent error is multiplying base × height and stopping. Always divide by 2.
• Mixing units. If the base is in cm and the height in m, convert one first. The area unit is the square of the unit you use (e.g. cm × cm = cm²).
• Confusing area with perimeter. Area is the space inside (square units); perimeter is the distance around (length units).

Limits of the Formula

This formula assumes the height is known. If you only have the three side lengths, you cannot directly apply it. Also, the formula gives the area in square units; for a triangle with base 10 m and height 6 m, the area is 30 m², not 30 m.

For very large or very small triangles, the same formula works, but be careful with unit conversions. For example, 1 m = 100 cm, so 1 m² = 10,000 cm².

Frequently Asked Questions

Why do we divide by 2?

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 equal triangles. So the triangle’s area is half the rectangle’s area (base × height), hence ½ × base × height.

What if the triangle is not right-angled?

The formula still works. Any triangle can be seen as half of a parallelogram (or rectangle) when you use the correct perpendicular height. The height may be inside or outside the triangle, but it is always at right angles to the base.

Can I use any side as the base?

Yes. Choose any side as the base, then measure the perpendicular height from that side to the opposite corner. The area will be the same regardless of which side you pick, as long as you use the matching height.

What if I only know the three side lengths?

You cannot use this simple formula. You would need to find the height first (using trigonometry or Heron’s formula), which is taught later, usually in secondary school. For KS2, the height is always given or can be measured.

How do I convert the area to different units?

Convert the base and height to the same unit first, then multiply and halve. For example, if base = 0.5 m and height = 20 cm, convert 0.5 m to 50 cm, then area = ½ × 50 × 20 = 500 cm². Alternatively, convert to metres: 20 cm = 0.2 m, area = ½ × 0.5 × 0.2 = 0.05 m². Both answers are correct (500 cm² = 0.05 m²).

What does the answer mean?

The area tells you how many square units fit inside the triangle. For example, 20 cm² means 20 squares of 1 cm by 1 cm would cover the triangle exactly. It is a measure of surface, not distance.

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in b | Base | cm | 8 | 0
in h | Height | cm | 5 | 0
out area | Area | cm² | 0.5 * b * h | 2