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  2. List of centroids - Wikipedia

    en.wikipedia.org/wiki/List_of_centroids

    Area rectangle area General triangular area + + [1] ... h = the height of the prism's triangular base L = the length of the prism see above for general

  3. List of second moments of area - Wikipedia

    en.wikipedia.org/wiki/List_of_second_moments_of_area

    A filled rectangular area as above but with respect to an axis collinear with the base = = [4] This is a result from the parallel axis theorem: A hollow rectangle with an inner rectangle whose width is b 1 and whose height is h 1

  4. Prism (geometry) - Wikipedia

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

    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.

  5. Semicircle - Wikipedia

    en.wikipedia.org/wiki/Semicircle

    For a semicircle with a diameter of a + b, the length of its radius is the arithmetic mean of a and b (since the radius is half of the diameter). The geometric mean can be found by dividing the diameter into two segments of lengths a and b, and then connecting their common endpoint to the semicircle with a segment perpendicular to the diameter ...

  6. Stadium (geometry) - Wikipedia

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

    A stadium is a two-dimensional geometric shape constructed of a rectangle with semicircles at a pair of opposite sides. [1] The same shape is known also as a pill shape, [2] discorectangle, [3] obround, [4] [5] or sausage body. [6] The shape is based on a stadium, a place used for athletics and horse racing tracks.

  7. Cavalieri's principle - Wikipedia

    en.wikipedia.org/wiki/Cavalieri's_principle

    From the definition of a cycloid, it has width 2πr and height 2r, so its area is four times the area of the circle. Calculate the area within this rectangle that lies above the cycloid arch by bisecting the rectangle at the midpoint where the arch meets the rectangle, rotate one piece by 180° and overlay the other half of the rectangle with it.

  8. Second moment of area - Wikipedia

    en.wikipedia.org/wiki/Second_moment_of_area

    An arbitrary shape. ρ is the distance to the element dA, with projections x and y on the x and y axes.. The second moment of area for an arbitrary shape R with respect to an arbitrary axis ′ (′ axis is not drawn in the adjacent image; is an axis coplanar with x and y axes and is perpendicular to the line segment) is defined as ′ = where

  9. Area - Wikipedia

    en.wikipedia.org/wiki/Area

    A = lw (rectangle). That is, the area of the rectangle is the length multiplied by the width. As a special case, as l = w in the case of a square, the area of a square with side length s is given by the formula: [1] [2] A = s 2 (square). The formula for the area of a rectangle follows directly from the basic properties of area, and is sometimes ...