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An equilateral triangle is a triangle in which all three sides have the same length, ... has a height of /, the sine of 60°. The area of an equilateral ...
For any interior point P, the sum of the lengths of the perpendiculars s + t + u equals the height of the equilateral triangle.. Viviani's theorem, named after Vincenzo Viviani, states that the sum of the shortest distances from any interior point to the sides of an equilateral triangle equals the length of the triangle's altitude. [1]
The length of the altitude, often simply called "the altitude" or "height", symbol h, is the distance between the foot and the apex. ... Equilateral triangle
Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two sides having the same length is an isosceles triangle, [4] [a] and a triangle with three different-length sides is a scalene triangle. [7]
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.
The slant height of a right square pyramid is defined as the height of one of its isosceles triangles. It can be obtained via the Pythagorean theorem : s = b 2 − l 2 4 , {\displaystyle s={\sqrt {b^{2}-{\frac {l^{2}}{4}}}},} where l {\displaystyle l} is the length of the triangle's base, also one of the square's edges, and b {\displaystyle b ...
The height of an equilateral triangle with edge length 2 is √ 3. Also, the long leg of a 30-60-90 triangle with hypotenuse 2. And, the height of a regular hexagon with sides of length 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]
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