Wedge (geometry)

Wedge with base , edge and height ${\displaystyle a,b}$ ${\displaystyle c}$ ${\displaystyle h}$

A wedge is a geometric body whose shape resembles a wedge and which is assigned to the prismatoids . Its base consists of a rectangle which is opposed to a single parallel (top) edge, which is connected to the base by two trapezoids and two triangles .

The volume of a wedge is:

${\displaystyle V={\frac {1}{6}}bh(2a+c)}$.

Here and are the side lengths of the rectangle, the length of the (top) edge and the height of the (top) edge above the base area. ${\displaystyle a}$ ${\displaystyle b}$ ${\displaystyle c}$ ${\displaystyle h}$

The height of the center of gravity above the base is:

${\displaystyle z={\frac {h(a+c)}{2(2a+c)}}}$.

In a coordinate system, it corresponds to the z coordinate of the center of gravity if the base area lies in the xy plane.

literature

• George R. Perkins: Plane and Solid Geometry . Appleton & Co, New York, 1854, p. 115
• John W. Harris, Horst Stöcker: Handbook of Mathematics and Computational Science . Springer 1998, ISBN 9780387947464 , p. 102

Web links

• Eric W. Weisstein : Wedge . In: MathWorld (English).