Calculations at an isosceles and right triangle. Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:
c = √2 * a
h_{c} = m_{c} = √2 * a / 2
h_{a} = h_{b} = a = b
m_{a} = √5 * a / 2
p = ( 2 + √2 ) * a
A = a² / 2
r_{c} = a / √2
r_{i} = a / (2 + √2 )
Hypotenuse angles: 45°

Catheti (legs), hypotenuse, median lines, heights, perimeter and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

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Side a and b, the catheti (legs), have the same length. The triangle is axially symmetric to the height h_{c}, this is identical to median line s_{c}. Heights h_{a} and h_{b} are identical to the sides b and a. The centroid is at the intersection of the median lines.

perimeter p, area A

sides and angles

heights

median lines and centroid

perpendicular bisectors and circumcircle

bisecting lines and incircle

In addition to the right angle, the isosceles and right triangle has two angles of 45 degrees each. It corresponds to a diagonally halved square, where the diagonal of the square is the hypotenuse of the triangle. Sometimes it is simply referred to as a half square. It is a special case of the isosceles triangle and the right triangle and can be viewed as the most regular triangle after the equilateral triangle.
This particular triangle is often encountered as a design element when a square is divided into two different colored triangles of this type. If you cut a square in half diagonally and put both halves together at the sides instead of at the hypotenuse so that they form the axis of symmetry, you get an isosceles right triangle that is twice as large. This, when reflected at the newly created hypotenuse, results in a square that has twice the area of the original. This way you can easily turn a square into a square that is twice as big. In the following picture you can see a square made up of four such isosceles right triangles.