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In geometry, calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is where b is the length of the base of the triangle, and h is the height or altitude of the triangle. The term "base" denotes any side, and "height" denotes the length of a perpendicular ...
Heron's formula. 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] It is named after first-century engineer Heron of Alexandria (or Hero) who ...
The three splitters of a triangle all intersect each other at the Nagel point of the triangle. A cleaver of a triangle is a segment from the midpoint of a side of a triangle to the opposite side such that the perimeter is divided into two equal lengths. The three cleavers of a triangle all intersect each other at the triangle's Spieker center.
The length of the internal bisector of the angle opposite the side of length a is [1] In a right triangle, the radius of the excircle on the hypotenuse equals the semiperimeter. The semiperimeter is the sum of the inradius and twice the circumradius. The area of the right triangle is where a, b are the legs.
In geometry, a Heronian triangle (or Heron triangle) is a triangle whose side lengths a, b, and c and area A are all positive integers. [1][2] Heronian triangles are named after Heron of Alexandria, based on their relation to Heron's formula which Heron demonstrated with the example triangle of sides 13, 14, 15 and area 84.
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero- dimensional points while the sides connecting them, also called edges, are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of ...
Properties. convex, cyclic. Dual polygon. Self-dual. In geometry, an isosceles triangle (/ aɪˈsɒsəliːz /) is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral ...
The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2] It is called the shoelace formula because of the constant cross-multiplying for the coordinates making up the ...
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