Area of a Triangle Formula
Geometry Formulas: Area, Volume, Perimeter
What is the formula for the area of a triangle?
Answer
Area of a triangle
A = ½ · a · h
Here a is the side (or base), h is the height, perpendicular to the base. The result comes out in square units.
Where the formula comes from
A = ½ · a · h
Take a second copy of the triangle, turn it 180° and join it to the first along one side: the two together make a parallelogram with base a and height h. The triangle is exactly half of it.
Worked examples
Let a = 10, h = 6. Then the area of a triangle = 30 square units.
Let a = 7.5, h = 4. Then the area of a triangle = 15 square units.
The common mistake
Using a slanted side as the height. The height is the perpendicular distance from the base to the opposite vertex, and in an obtuse triangle the two heights drawn to the sides next to the obtuse angle fall outside the triangle — you have to extend the base to meet them.
Other quantities: Triangle
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See Also
- Square Footage Calculator - Width × length in feet to square feet
- Square Feet to Square Meters (Sq Ft to Sq M) - Convert Square Feet to Square Meters
- Square Meters to Square Feet (Sq M to Sq Ft) - Convert Square Meters to Square Feet
- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
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Values from the Formula (h = 6)
| If a = | Area |
|---|---|
| 1 | 3 square units |
| 2 | 6 square units |
| 3 | 9 square units |
| 4 | 12 square units |
| 5 | 15 square units |
| 10 | 30 square units |
Geometry Formulas: Area, Volume, Perimeter
These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the area of a triangle? (The answer is: A = ½ · a · h). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter