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Every equable triangle has an inradius of 2. [1] [2] A two-dimensional equable shape (or perfect shape) is one whose area is numerically equal to its perimeter. [3] For example, a right angled triangle with sides 5, 12 and 13 has area and perimeter both with a unitless numerical value of 30.
Three of them are the medians, which are the only area bisectors that go through the centroid. Three other area bisectors are parallel to the triangle's sides. Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter. There can be one, two, or three of these for any given ...
The interior angles of an ideal triangle are all zero. An ideal triangle has infinite perimeter. An ideal triangle is the largest possible triangle in hyperbolic geometry. In the standard hyperbolic plane (a surface where the constant Gaussian curvature is −1) we also have the following properties: Any ideal triangle has area π. [1]
A triangle with sides a, b, and c. In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths , , . Letting be the semiperimeter of the triangle, = (+ +), the area is [1]
The only triangle with consecutive integers for an altitude and the sides is acute, having sides (13,14,15) and altitude from side 14 equal to 12. The smallest-perimeter triangle with integer sides in arithmetic progression, and the smallest-perimeter integer-sided triangle with distinct sides, is obtuse: namely the one with sides (2, 3, 4).
Each edge interior to the polygon is the side of two triangles. However, there are b {\displaystyle b} edges of triangles that lie along the polygon's boundary and form part of only one triangle. Therefore, the number of sides of triangles obeys the equation 6 A = 2 E − b {\displaystyle 6A=2E-b} , from which one can solve for the number of ...
The three splitters concur at the Nagel point of the triangle. A cleaver of a triangle is a line segment that bisects the perimeter of the triangle and has one endpoint at the midpoint of one of the three sides. So any cleaver, like any splitter, divides the triangle into two paths each of whose length equals the semiperimeter.
The interior perpendicular bisector of a side of a triangle is the segment, falling entirely on and inside the triangle, of the line that perpendicularly bisects that side. The three perpendicular bisectors of a triangle's three sides intersect at the circumcenter (the center of the circle through the three vertices). Thus any line through a ...