Triangle Side Calculator
Find the missing sides of a triangle using the triangle side calculator.
Area20.333163from sides 6, 7, 8
Area20.333163
Perimeter21
Sides6, 7, 8
Angles46.5675°, 57.91°, 75.5225°
TypeAcute scalene
Inradius1.936492
Circumradius4.131182
Working
| Semi-perimeter s | 10.5 |
| Area (Heron) | √(s(s−a)(s−b)(s−c)) = 20.333163 |
| Height on side a | 2 × area ÷ a = 6.777721 |
| Inradius | area ÷ s = 1.936492 |
| Circumradius | abc ÷ 4·area = 4.131182 |
| Angle sum | 180° (always 180°) |
The formula
Heron: A = √(s(s−a)(s−b)(s−c)) with s = (a+b+c)/2
What always holds
- The three angles add to 180°, without exception.
- Any two sides must add to more than the third — the triangle inequality. Sides of 4, 5 and 12 cannot close.
- The longest side always faces the largest angle.
Area = ½ × base × heightfor any triangle, with the height measured perpendicular to that base.
Which formula to reach for
With three sides, use Heron’s formula. With a base and its height, use ½bh. With two sides and the angle between them, use ½ab·sin C. With a right angle, the two legs are already base and height, so the area is just half their product.