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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 ...
Schläfli symbol. {3} (for equilateral) Area. various methods; see below. 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.
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
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 proved it in his ...
The polygon area consists of n equal triangles with height h and base s, thus equals 1 ⁄ 2 nhs. But since h < r and ns < c, the polygon area must be less than the triangle area, 1 ⁄ 2 cr, a contradiction. Therefore, our supposition that C might be greater than T must be wrong.
Incircle and excircles. Incircle and excircles of a triangle. In geometry, the incircle or inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter. [ 1] An excircle or escribed circle[ 2 ...
The following is a list of second moments of area of some shapes. The second moment of area, also known as area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with respect to an arbitrary axis. The unit of dimension of the second moment of area is length to fourth power, L 4, and should not ...
For an equilateral triangle: The ratio of its area to the area of the incircle, , is the largest of any triangle. [21]: Theorem 4.1 The ratio of its area to the square of its perimeter, , is larger than that of any non-equilateral triangle. [11]