Here, a skewed cuboid is a hexahedron with two opposite rectangles, where one vertex is right above the other. One of the rectangles (here the bottom) has length and width larger or equal than the other. Other faces are right trapezoids. Front and right face are skewed, left and rear face are straight. The volume is calculated from the cuboid of the smaller rectangle, two ramps and one corner.
Enter length and width of the rectangles and the height, choose the number of decimal places, then click Calculate.
Formulas:
e = √ c² + d² + h²
f1 = √ a² + d² + h²
f2 = √ c² + b² + h²
g = √ a² + b² + h²
r = √ (d-b)² + h²
s = √ (d-b)² + (c-a)² + h²
t = √ (c-a)² + h²
A1 = a * b
A2 = c * d
A3 = h * ( b + d ) / 2
A4 = h * ( a + c ) / 2
A5 = t * ( b + d ) / 2
A6 = r * ( a + c ) / 2
A = A1 + A2 + A3 + A4 + A5 + A6
V = abh + h(d-b)a/2 + h(c-a)b/2 + (c-a)(d-b)h/6
Lengths, widths, height and diagonals have the same unit (e.g. meter), the areas have this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit -1.
The lengths a and c are parallel to each other, as are the lengths b and d. This does not appear so in the image above, as the slanted cuboid is distorted in that the closer parts appear larger, as is natural perception. This is to better recognize the properties of the slanted sides.
There are two of each length a, b, c, and d; there are right angles between a and b, as well as c and d. Right angles are also found between h and a and b, and between h and c and d. The other angles are less than or greater than 90 degrees. The diagonals are calculated like the space diagonal of a cuboid. The surface area is the sum of the six side surfaces.
Bricks of this shape are used in construction for corners that taper towards the top. An example would be the bottom corners of a perfect pyramid.
