Wedge Calculator

Name: Wedge - Geometry Calculator
Author: Jürgen Kummer

Calculations at a wedge with rectangular base and an apex edge c, which is shorter than the base edges a and is centrically above the base. a and b are perpendicular to each other, a and c are parallel.
Enter the three lengths a, b and c and the height h and choose the number of decimal places. Then click Calculate.

Formulas:

s = \sqrt{h^{2} + {(\frac{a - c}{2})}^{2} + {(\frac{b}{2})}^{2}}

A = a b + (a + c) \cdot \sqrt{s^{2} - {(\frac{a - c}{2})}^{2}} + b \cdot \sqrt{\frac{4 s^{2} - b^{2}}{4}}

V = b h \cdot (\frac{a}{3} + \frac{c}{6})

Lengths, width and height have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter).

The term wedge is used in everyday use as well as in geometry and describes roughly the same shape. In a general wedge, two opposite sides extend from the rectangular base, which taper towards each other. There are several special forms of wedge, this is one of them with the conditions mentioned above. Other special forms are the right wedge, in which the non-tapering sides are parallel, and the ramp, in which the parallel sides also have a right angle to one of the tapering sides. The half tetrahedron is also a special wedge. The wedge itself is a special form of the prismatoid.

Wedges are used as splitting tools, for example. The pointed edge of the wedge is placed in a gap and then force is applied to the base to enlarge the gap. Knives work on the same principle. A wedge in the form of a ramp is the wedge-shaped doorstop, which rests on the side with the longer leg and where the door is stopped by the hypotenuse side. Wedges are ancient tools in the history of mankind; hand axes in wedge form were already used in the Stone Age two million years ago.

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