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In Euclidean geometry, an equidiagonal quadrilateral is a convex quadrilateral whose two diagonals have equal length. Equidiagonal quadrilaterals were important in ancient Indian mathematics , where quadrilaterals were classified first according to whether they were equidiagonal and then into more specialized types.
The volume of a pyramid is the one-third product of the base's area and the height. The pyramid height is defined as the length of the line segment between the apex and its orthogonal projection on the base. Given that is the base's area and is the height of a pyramid, the volume of a pyramid is: [25] =.
This is a list of volume formulas of basic ... and is the prism's height; Pyramid – , where is ... area and is the pyramid's height; Tetrahedron ...
The volume of a prism is the product of the area of the base by the height, i.e. the distance between the two base faces (in the case of a non-right prism, note that this means the perpendicular distance). The volume is therefore: =, where B is the base area and h is the height.
A volume is a measurement of a region in three-dimensional space. [12] The volume of a polyhedron may be ascertained in different ways: either through its base and height (like for pyramids and prisms), by slicing it off into pieces and summing their individual volumes, or by finding the root of a polynomial representing the polyhedron. [13]
Among all quadrilaterals, the shape that has the greatest ratio of its perimeter to its diameter (maximum distance between any two points) is an equidiagonal kite with angles 60°, 75°, 150°, 75°. Its four vertices lie at the three corners and one of the side midpoints of the Reuleaux triangle .
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 ...
A quadric quadrilateral is a convex quadrilateral whose four vertices all lie on the perimeter of a square. [7] A diametric quadrilateral is a cyclic quadrilateral having one of its sides as a diameter of the circumcircle. [8] A Hjelmslev quadrilateral is a quadrilateral with two right angles at opposite vertices. [9]