Isosceles Triangle Calculator

Name: Isosceles Triangle - Geometry Calculator
Author: Jürgen Kummer

Calculations at an isosceles triangle. This is a triangle with two sides of equal length.
Enter two lengths and choose the number of decimal places. Then click Calculate. Angles are calculated and displayed in degrees, here you can convert angle units.

Formulas:

α = β = \arccos (\frac{c}{2 a})

γ = \arccos (\frac{2 \cdot a^{2} - c^{2}}{2 a^{2}})

h = h_{c} = \sqrt{\frac{4 \cdot a^{2} - c^{2}}{4}}

h_{a} = h_{b} = c \cdot \sin (β) = a \cdot \sin (γ)

p = 2 \cdot a + c

A = \frac{h \cdot c}{2}

r_{c} = \frac{4 \cdot h^{2} + c^{2}}{8 \cdot h}

r_{i} = \frac{c \cdot h}{2 a + c}

m_{a} = m_{b} = \frac{\sqrt{a^{2} + 2 \cdot c^{2}}}{2}

m_{c} = \frac{\sqrt{4 \cdot a^{2} - c^{2}}}{2}

Lengths, height, median lines and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

Side a and b, the legs, have the same length. The isosceles triangle is axially symmetric to the height h_c.The centroid is at the intersection of the median lines. The intersections of the heights, median lines, perpendicular bisectors and bisecting lines lie all on height h_c, on different locations.

perimeter p, area A

sides and angles

heights

median lines and centroid

perpendicular bisectors and circumcircle

bisecting lines and incircle

More regular than the isosceles is the equilateral triangle. In this case, not two, but all three sides are the same length and not two, but all three angles are the same size. The equilateral triangle has angles of sixty degrees each, so an isosceles triangle that is not equilateral does not have any angle of sixty degrees, but other values, which of course add up to 180 degrees. The isosceles triangle can be found on the side surfaces of the regular pyramid and the wedge, as well as of course the shapes based on them, such as the regular bipyramid and the right wedge. Convex bodies with identical isosceles triangles as side surfaces are the Catalan solids triakis tetrahedron, triakis octahedron, tetrakis hexahedron and triakis icosahedron. Two concave bodies that only have identical isosceles triangles as side surfaces are the small stellated dodecahedron and the great dodecahedron. The great icosahedron, on the other hand, has equilateral triangles as side faces.

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