Triangle Area Calculator
The area of any triangle from its base and height.
- Area30.0000
Inputs used
- Base10
- Height (perpendicular)6
About this calculator
A triangle's area is half its base times its height: A = ½ × b × h. The height must be measured perpendicular to the base — the straight-line distance from the base to the opposite corner, not the length of a slanted side.
Any side can serve as the base; pick whichever one you know the perpendicular height for. The ½ appears because every triangle is exactly half of the parallelogram you'd get by duplicating and rotating it.
Only have the three side lengths? Heron's formula covers that case: with s as half the perimeter, A = √(s(s−a)(s−b)(s−c)).
Quick reference
Area by base and height
Area A = ½ × base × height for each base (rows) and perpendicular height (columns).
| Base | 3 | 4 | 5 | 6 | 8 | 10 |
|---|---|---|---|---|---|---|
| 4 | 6.0000 | 8.0000 | 10.0000 | 12.0000 | 16.0000 | 20.0000 |
| 5 | 7.5000 | 10.0000 | 12.5000 | 15.0000 | 20.0000 | 25.0000 |
| 6 | 9.0000 | 12.0000 | 15.0000 | 18.0000 | 24.0000 | 30.0000 |
| 8 | 12.0000 | 16.0000 | 20.0000 | 24.0000 | 32.0000 | 40.0000 |
| 10 | 15.0000 | 20.0000 | 25.0000 | 30.0000 | 40.0000 | 50.0000 |
| 12 | 18.0000 | 24.0000 | 30.0000 | 36.0000 | 48.0000 | 60.0000 |
| 15 | 22.5000 | 30.0000 | 37.5000 | 45.0000 | 60.0000 | 75.0000 |
| 20 | 30.0000 | 40.0000 | 50.0000 | 60.0000 | 80.0000 | 100.0000 |
Frequently asked questions
What is the formula for the area of a triangle?
Half the base times the height: A = ½ × b × h. A triangle with a base of 10 and a height of 6 has an area of ½ × 10 × 6 = 30 square units.
Does the height have to be perpendicular to the base?
Yes — the height is the straight-line distance from the base to the opposite corner, measured at a right angle to the base, not the length of a slanted side. Using a slant length overstates the area.
How do I find the area if I only know the three sides?
Use Heron's formula. Let s be half the perimeter, s = (a + b + c) ÷ 2, then A = √(s(s−a)(s−b)(s−c)). It needs no height at all.
Why is there a ½ in the triangle area formula?
Because a triangle is exactly half of the parallelogram formed by duplicating it and rotating the copy 180°. The parallelogram has area base × height, so the triangle has half of that.
Embed this calculator on your site
Paste this HTML where you want the calculator to appear. It stays free, works on any site, and updates automatically. Adjust the height to taste.
Results are informational only — not financial, medical or legal advice.