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  2. Area of a triangle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_triangle

    The area of a triangle can be demonstrated, for example by means of the congruence of triangles, as half of the area of a parallelogram that has the same base length and height. A graphic derivation of the formula T = h 2 b {\displaystyle T={\frac {h}{2}}b} that avoids the usual procedure of doubling the area of the triangle and then halving it.

  3. Heron's formula - Wikipedia

    en.wikipedia.org/wiki/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]

  4. Triangle - Wikipedia

    en.wikipedia.org/wiki/Triangle

    The area formula for a triangle can be proven by cutting two copies of the triangle into pieces and rearranging them into a rectangle. In the Euclidean plane, area is defined by comparison with a square of side length ⁠ ⁠, which has area 1. There are several ways to calculate the area of an arbitrary triangle.

  5. Pick's theorem - Wikipedia

    en.wikipedia.org/wiki/Pick's_theorem

    Any triangle subdivides its bounding box into the triangle itself and additional right triangles, and the areas of both the bounding box and the right triangles are easy to compute. Combining these area computations gives Pick's formula for triangles, and combining triangles gives Pick's formula for arbitrary polygons. [7] [8] [13]

  6. Brahmagupta's formula - Wikipedia

    en.wikipedia.org/wiki/Brahmagupta's_formula

    This formula generalizes Heron's formula for the area of a triangle. A triangle may be regarded as a quadrilateral with one side of length zero. From this perspective, as d approaches zero, a cyclic quadrilateral converges into a cyclic triangle (all triangles are cyclic), and Brahmagupta's formula simplifies to Heron's formula.

  7. Solution of triangles - Wikipedia

    en.wikipedia.org/wiki/Solution_of_triangles

    A triangle can be uniquely determined in this sense when given any of the following: [1] [2] Three sides (SSS) Two sides and the included angle (SAS, side-angle-side) Two sides and an angle not included between them (SSA), if the side length adjacent to the angle is shorter than the other side length. A side and the two angles adjacent to it (ASA)

  8. Barycentric coordinate system - Wikipedia

    en.wikipedia.org/wiki/Barycentric_coordinate_system

    If a point lies on an edge of the triangle but not at a vertex, one of the area coordinates (the one associated with the opposite vertex) is zero, while the other two lie in the open interval (,). If the point lies on a vertex, the coordinate associated with that vertex equals 1 and the others equal zero.

  9. Area - Wikipedia

    en.wikipedia.org/wiki/Area

    This formula is also known as the shoelace formula and is an easy way to solve for the area of a coordinate triangle by substituting the 3 points (x 1,y 1), (x 2,y 2), and (x 3,y 3). The shoelace formula can also be used to find the areas of other polygons when their vertices are known.