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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.
A right triangle ABC with its right angle at C, hypotenuse c, and legs a and b,. A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle (1 ⁄ 4 turn or 90 degrees).
An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it; this is the exterior angle theorem. [34]
The general spherical triangle is fully determined by three of its six characteristics (3 sides and 3 angles). The lengths of the sides a, b, c of a spherical triangle are their central angles, measured in angular units rather than linear units. (On a unit sphere, the angle (in radians) and length around the sphere are numerically the same. On ...
Since the area of a triangle cannot be negative the spherical excess is always positive. It is not necessarily small, because the sum of the angles may attain 5 π (3 π for proper angles). For example, an octant of a sphere is a spherical triangle with three right angles, so that the excess is π /2.
The trigonometry formulas of right triangles also give the relations between the sides s and the angles A of an equilateral triangle (a triangle where all sides have the same length and all angles are equal). The relations are: = ()
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]
If the legs have lengths a, b, c, then the trirectangular tetrahedron has the volume [2] =. The altitude h satisfies [3] = + +. The area of the base is given by [4] =. The solid angle at the right-angled vertex, from which the opposite face (the base) subtends an octant, has measure π /2 steradians, one eighth of the surface area of a unit sphere.