Case 1
- Base
- 10
- Height
- 6
30.00
Open with these valuesTriangle Area Calculator
30.00square units
Result: 30.00 square unitsBase times perpendicular height, halved. A triangle with a base of 10 and a height of 6 covers 30 square units — exactly half the parallelogram with the same base and height. Any of the three sides can be the base, as long as the height is measured at a right angle to it.
The numbers at a glance
Held fixed: Base 10.000.
| Height | Result |
|---|---|
| 2.000 | 10.00 |
| 4.000 | 20.00 |
| 6.000Your value | 30.00 |
| 8.000 | 40.00 |
| 10.000 | 50.00 |
| 12.000 | 60.00 |
Worked examples
Case 2
- Base
- 7
- Height
- 3
10.50
Open with these valuesCase 3
- Base
- 1
- Height
- 1
0.50
Open with these valuesHow it's calculated
A = (base × height) ÷ 2
- StepChoose one side as the base — whichever is easiest to measure.
- StepMeasure straight from that base to the opposite corner, at a right angle.
- ResultRead the area in the square of the unit you entered.
What this number means
The height is not a slanted side
It is the straight-line distance from the chosen base to the opposite corner, measured at a right angle to that base. Reaching for a sloping side instead makes the area come out too large.
Any of the three sides can be the base
Pick whichever side is easiest to measure and pair it with the height perpendicular to that side. All three pairings give exactly the same area.
Half a parallelogram
A triangle covers exactly half of the parallelogram built on the same base and the same height. That is where the ÷ 2 comes from: base 10 with height 6 gives 30 square units.
Three sides but no height? Heron instead
Take the semi-perimeter s = (a + b + c) ÷ 2, then area = √(s × (s − a) × (s − b) × (s − c)). It needs no perpendicular height at all.
Commonly misread
A triangle with sides of 10 and 6 has an area of 30.
Only if the 6 is the height measured at a right angle to the 10. A second side length is not a height, and the area would come out too large.
The base has to be the side the triangle sits on.
Any of the three sides can be the base. What matters is that the height belongs to that same side and meets it at a right angle.
Base in metres and height in centimetres is fine — the calculator is unit-agnostic.
Unit-agnostic means it takes any unit, not two at once. Enter both lengths in the same unit and read the area in the square of it.
Reference table
| Base, height | Worked out | Area |
|---|---|---|
| 1, 1 | 1 × 1 ÷ 2 | 0.5 |
| 4, 5 | 4 × 5 ÷ 2 | 10 |
| 7, 3 | 7 × 3 ÷ 2 | 10.5 |
| 10, 6 | 10 × 6 ÷ 2 | 30 |
| 12, 8 | 12 × 8 ÷ 2 | 48 |
Questions
How do I calculate the area of a triangle?
Multiply the base by the perpendicular height and divide by two: area = (base × height) ÷ 2. A triangle with a base of 10 and a height of 6 has an area of 30 square units.
Which height should I measure?
The perpendicular height — the straight-line distance from the chosen base to the opposite corner, measured at a right angle to that base. It is not the length of a slanted side. Using a sloping side by mistake makes the area come out too large.
Can any side be the base?
Yes. Any of the three sides can serve as the base, as long as you pair it with the height measured perpendicular to that side. All three pairs give exactly the same area, so pick whichever is easiest to measure.
What if I only know the three side lengths?
When you know all three sides but no height, use Heron's formula instead. Take the semi-perimeter s = (a + b + c) ÷ 2, then area = √(s × (s − a) × (s − b) × (s − c)). It gives the same answer without ever needing a perpendicular height.
What units does the result use?
The calculator is unit-agnostic: the area comes out in the square of whatever unit you entered. Base and height in metres give square metres, in inches square inches. Just keep both in the same unit.
Sources and last check
Information, not professional advice.