Isosceles Triangle Find A Calculator
This isosceles triangle find A calculator is designed to help you find the missing side and angles of a triangle given two values.
Area12
Height to the base4
Area12
Perimeter16
Sides5, 5, 6
Angles53.1301°, 53.1301°, 73.7398°
TypeAcute isosceles
Inradius1.5
Circumradius3.125
Working
| Semi-perimeter s | 8 |
| Area (Heron) | √(s(s−a)(s−b)(s−c)) = 12 |
| Height on side a | 2 × area ÷ a = 4.8 |
| Inradius | area ÷ s = 1.5 |
| Circumradius | abc ÷ 4·area = 3.125 |
| Angle sum | 180° (always 180°) |
The formula
two equal legs, base b: h = √(leg² − (b/2)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.