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2. Tetrahedron - Wikipedia

   en.wikipedia.org/wiki/Tetrahedron

   The volume of a tetrahedron can be obtained in many ways. It can be given by using the formula of the pyramid's volume: =. where is the base' area and is the height from the base to the apex. This applies for each of the four choices of the base, so the distances from the apices to the opposite faces are inversely proportional to the areas of ...

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

   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]

5. Rhombicosidodecahedron - Wikipedia

   en.wikipedia.org/wiki/Rhombicosidodecahedron

   For a rhombicosidodecahedron with edge length a, its surface area and volume are: = ... Triangle Face Pentagon Solid Wireframe Projective symmetry [2] [2] [2] [2] [6]

6. Pick's theorem - Wikipedia

   en.wikipedia.org/wiki/Pick's_theorem

   Because each special triangle has area , a polygon of area will be subdivided into special triangles. [ 5 ] The subdivision of the polygon into triangles forms a planar graph , and Euler's formula V − E + F = 2 {\displaystyle V-E+F=2} gives an equation that applies to the number of vertices, edges, and faces of any planar graph.

7. Hyperpyramid - Wikipedia

   en.wikipedia.org/wiki/Hyperpyramid

   The n-dimensional volume of a n-dimensional hyperpyramid can be computed as follows: = Here V n denotes the n-dimensional volume of the hyperpyramid, A the (n – 1)-dimensional volume of the base and h the height, that is the distance between the apex and the (n – 1)-dimensional hyperplane containing the base A.

8. The Method of Mechanical Theorems - Wikipedia

   en.wikipedia.org/wiki/The_Method_of_Mechanical...

   The condition of balance ensures that the volume of the cone plus the volume of the sphere is equal to the volume of the cylinder. The volume of the cylinder is the cross section area, times the height, which is 2, or . Archimedes could also find the volume of the cone using the mechanical method, since, in modern terms, the integral involved ...

9. Pyramid (geometry) - Wikipedia

   en.wikipedia.org/wiki/Pyramid_(geometry)

   Given that is the base's area and is the height of a pyramid, the volume of a pyramid is: [25] =. The volume of a pyramid was recorded back in ancient Egypt, where they calculated the volume of a square frustum, suggesting they acquainted the volume of a square pyramid. [26]