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Enter any three known attributes (ensuring at least one side is included) into the fields below, then click "Calculate". If radians are chosen as the angle unit, entries like pi/2 or pi/4 are accepted.
In geometry, a triangle functions as a fundamental polygon characterized by three distinct vertices and edges. Typically, any given triangle featuring corners labeled A, B, and C is designated mathematically as $\triangle ABC$.
Triangles are generally categorized based on their internal angles and side lengths:
Several mathematical rules govern the relationships within any standard triangle:
Depending on available metrics, multiple formulas can determine surface area. The traditional approach utilizes base and altitude: $\text{Area} = \frac{1}{2}bh$. Alternatively, when all three side lengths are available, Heron's formula $\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$ is applied using the semi-perimeter $s$.
Because an isosceles configuration features matching sides and angles, specialized equations help compute its specific height, perimeter, and area values:
$\text{Area} = \frac{1}{2} b \sqrt{a^2 - \frac{b^2}{4}}$
Medians: Line segments linking any corner vertex directly to the center point of the opposing side, dividing the main shape into two equal-area sections.
Inradius ($r$): Denotes the radius length of an inner circle perfectly enclosed inside the triangle, computed via $r = \frac{\text{Area}}{s}$.
Circumradius ($R$): Refers to the radius of an outer circle intersecting all three outer vertices, formulated as $R = \frac{abc}{4 \times \text{Area}}$.
The orthocenter represents the single intersecting point where all three altitudes (perpendicular lines dropped from each vertex to the opposite side) of a triangle meet. Depending on whether the triangle is acute, right, or obtuse, the orthocenter can reside inside, directly on a vertex, or outside the boundary of the shape.
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