Key takeaways
- The area of a triangle is A = ½ × b × h.
- Height must be measured at a right angle to the base, never along a slanted side.
- A triangle is exactly half of the rectangle formed by the same base and height.
- If you only know the three sides, use Heron's formula instead.
In this guide
What is the area of a triangle?
A triangle is a three-sided shape. Its area is the flat space inside it, measured in square units such as cm² or m². This formula works for any triangle, as long as you know its base and height.
Why does the area of a triangle matter?
Triangles are the building block behind roof gables, sails, flags, and structural trusses. Whatever their shape, area only depends on base and height.
A right triangle and a very leaning, obtuse triangle can both have a base of 6 and a height of 4 — and both will cover exactly the same 12 square units, even though one looks far more "tilted" than the other.
The formula
| Symbol | What it means | Example |
|---|---|---|
| A | The area you want to find | 12 m² |
| b | The base: the side you're measuring from | 6 m |
| h | The height: perpendicular distance from base to opposite corner | 4 m |
How to find the area step by step
- 1Choose a base. Any side can be the base; pick whichever is easiest to measure.
- 2Measure the height. Find the perpendicular distance from that base to the opposite corner.
- 3Multiply base by height.
b × h. - 4Divide by 2. A triangle is always half of the matching rectangle.
Now try it yourself. Change the base and height in the calculator below and watch the area update, with every step shown.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Forgetting to divide by 2. Multiplying base by height alone gives the area of the full rectangle, not the triangle.
- Not having a height at all. If you only know the three side lengths, use Heron's formula calculator instead.
- Mixing up base and height. Either side can be the base, as long as the height is perpendicular to whichever one you pick.
Tips and tricks
- To find a missing side of a right triangle first, use the Pythagorean theorem calculator.
- Working backwards from area? Multiply by 2 and divide by the known base or height:
h = (2 × A) ÷ b.
Where you'll use it in real life
- Sewing and crafts: sizing a triangular flag or shade sail.
- Construction: estimating paint or siding for a triangular gable wall.
- Landscaping: working out the area of a triangular garden plot.
- Design: calculating material for triangular signage or bunting.
Quick summary
To find the area of a triangle, multiply the base by the perpendicular height, then divide by 2. Always measure the height at a right angle to the base, never along a slanted side. Use the calculator above to check your own triangle in seconds.
Worked example
You're making a triangular shade sail for a patio with a base of 6 meters and a height of 4 meters. How much fabric do you need?
- 01A = ½bh
- 02A = ½ × 6 × 4
- 03A = ½ × 24
- 04A = 12 m²
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I find the area of a triangle if I only know the three sides?
Use Heron's formula instead, which calculates area directly from the three side lengths without needing a height. Try the [Heron's formula calculator](/calculator/herons-formula).
Does it matter which side I call the base?
No, any side can be the base, as long as you measure the height as the perpendicular distance from that same side to the opposite corner.
Why do we divide by 2 in the triangle area formula?
A triangle is exactly half of a rectangle (or parallelogram) with the same base and height, so its area is half of base × height.
How is triangle area different from perimeter?
Area (½bh) is the space inside, in square units. Perimeter is the total length of all three sides added together — see the [perimeter of a triangle calculator](/calculator/perimeter-triangle).
