Advanced Triangle Calculator & Concepts Guide
Calculate missing sides, internal angles, area, perimeter, medians, inradius, and circumradius instantly with dynamic visual representation and comprehensive conceptual tables.
Please provide 3 values (including at least one side) into the fields around the triangle below, and click "Calculate".
Comprehensive Triangle Concepts & Classifications
Triangles can be categorized based on their side lengths and interior angles. Below are detailed descriptions and concept tables explaining each type and geometric property.
1. Classification by Sides
Triangles are divided into three categories based on the relative equality of their side lengths:
| Triangle Type | Side Property | Angle Property | Type Result |
|---|---|---|---|
| Equilateral | All 3 sides are equal | All 3 angles are 60° | Regular / Symmetric |
| Isosceles | Exactly 2 sides are equal | Base angles are equal | Symmetric |
| Scalene | All 3 sides have different lengths | All 3 angles are different | Asymmetric |
2. Classification by Angles
Triangles can also be classified according to the measurements of their interior angles:
| Triangle Type | Angle Condition | Type Result |
|---|---|---|
| Right Triangle | One angle = 90° | Right-Angled Triangle (Pythagorean relation applies) |
| Obtuse Triangle | One angle > 90° | Obtuse-Angled Triangle |
| Acute Triangle | All angles < 90° | Acute-Angled Triangle |
3. Area, Medians, and Radius Properties
Advanced geometric properties such as medians, inradius, and circumradius help define the spatial and center properties of a triangle:
| Element / Property | Description & Definition | Intersection Point / Formula Result |
|---|---|---|
| Area & Base-Height | Calculated using base (b) and perpendicular height (h). Formula: Area = 1/2 × b × h | Square units of surface area |
| Medians (ma, mb, mc) | Line segments connecting vertices to the midpoints of opposite sides. | Centroid (Center of gravity) |
| Inradius (r) | Radius of the inscribed circle touching all three sides internally. | Incenter (Meeting point of angle bisectors) |
| Circumradius (R) | Radius of the circumscribed circle passing through all three vertices. | Circumcenter (Meeting point of perpendicular bisectors) |