How to Calculate the Square Footage of a Triangle

The square footage of a triangle is half its base times its height — ½ × base × height. The formula is short; the catch is that “height” isn’t a side you can usually just run a tape along. On a real triangular space it’s the perpendicular distance from the base to the far point, and measuring it is where people get stuck.

This guide covers the standard formula, the three-sides method for when the height is awkward to measure (including triangles with three unequal sides), and the right-triangle shortcut. The triangle calculator handles the first, the three-sides calculator the second.

Half the base times the height

Pick any side as the base. The height is the straight-line distance from that base to the opposite corner, measured at a right angle to the base — not along a slanted side. Multiply them and halve the result:

½ × base × height

A triangle with a 12-foot base and an 8-foot perpendicular height is ½ × 12 × 8 = 48 square feet. Any of the three sides can serve as the base, as long as you measure the height perpendicular to whichever one you chose — you’ll get the same area every time.

When you can’t measure the height: use three sides

The height is often the one measurement you can’t easily take — there’s furniture in the way, or the “point” of the triangle is a corner you can’t reach square-on. In that case, measure the three sides instead and use Heron’s formula:

1. Add the three sides and halve the total. For sides of 9, 12 and 15 feet: (9 + 12 + 15) ÷ 2 = 18. Call this s.
2. Work out s × (s − a) × (s − b) × (s − c): 18 × (18−9) × (18−12) × (18−15) = 18 × 9 × 6 × 3 = 2,916.
3. Take the square root: √2,916 = 54 square feet.

This works for any triangle, including one with three unequal sides where there’s no obvious base or height. The three-sides triangle calculator runs all three steps once you enter the sides.

Right triangles are the easy case

If the triangle has a square corner — a room where two walls meet at 90 degrees and a diagonal closes it off — you already have the base and height. The two sides that form the right angle are the base and height, so:

½ × side A × side B

A right-triangular nook with 6-foot and 9-foot walls at the corner is ½ × 6 × 9 = 27 square feet. No perpendicular measuring needed, because the two walls are already perpendicular.

Triangular spaces in practice

Triangles turn up more often as parts of a space than as whole rooms:

• Gable walls — the triangle above the eaves on a pitched roof, sitting on top of a rectangle. The wall square footage guide covers combining the two.
• Attic rooms and sloped ceilings — the floor may be rectangular, but the usable cross-section is often a triangle or trapezoid.
• Angled room corners — a rectangle with a triangular slice cut off; work out the rectangle and subtract the triangle.
• Triangular and pie-shaped lots — most irregular plots split into triangles, which is the backbone of calculating land square footage.

The mistakes to avoid

1. Forgetting the ½. Without it you’ve calculated the rectangle around the triangle — exactly double the real area.
2. Using a slanted side as the height. The height is the perpendicular distance to the base, not the length of the leaning side.
3. Mixing feet and inches. Convert inches to decimal feet (inches ÷ 12) before multiplying.
4. Forcing the base-height method when the height is unknown. Measure the three sides and use Heron’s formula instead.

Frequently asked questions

How do you calculate the square footage of a triangle?

Multiply the base by the height and divide by two: ½ × base × height, both in feet. The height has to be measured straight out from the base at a right angle, not along a sloping side. A 10-foot base with a 6-foot height gives ½ × 10 × 6 = 30 square feet.

How do you find the area of a triangle with three unequal sides?

Use Heron’s formula. Add the three sides and halve the total to get a value called s, then take the square root of s × (s − a) × (s − b) × (s − c). It works for any triangle, no height needed — which is why it’s the go-to for oddly shaped triangular rooms and lots.

What if I don’t know the height of the triangle?

Measure the three sides instead and use Heron’s formula, which gets the area from the side lengths alone. This is usually easier than the base-and-height method anyway, since the sides of a room or lot are simple to tape while the perpendicular height often isn’t reachable.

How do you find the square footage of a right triangle?

For a right triangle, the two sides that meet at the square corner are already the base and height, so just multiply them and halve: ½ × side A × side B. A right-triangular corner with 8-foot and 5-foot legs is ½ × 8 × 5 = 20 square feet.

Why do you divide a triangle’s area by two?

Because a triangle is exactly half of the rectangle that would enclose it. Base times height gives you that full rectangle; halving it leaves the triangle. It’s the step people most often skip, and skipping it doubles the answer.

The short version

A triangle’s square footage is straightforward once you know which method fits your measurements.

• Base × height ÷ 2 is the standard formula — measure the height perpendicular to the base.
• Can’t measure the height? Use the three side lengths with Heron’s formula.
• For a right triangle, the two sides at the square corner are the base and height.
• Never skip the ÷ 2, and convert inches to feet before multiplying.

Enter a base and height in the triangle calculator, or three sides in the three-sides calculator, and either one returns the area in square feet along with the other common units.