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Shape Figure ¯ ¯ Area rectangle area: General triangular area + + [1] Isosceles-triangular area: Right-triangular area: Circular area: Quarter-circular area [2]: Semicircular area [3]: Circular sector
Circle with square and octagon inscribed, showing area gap. Suppose that the area C enclosed by the circle is greater than the area T = cr/2 of the triangle. Let E denote the excess amount. Inscribe a square in the circle, so that its four corners lie on the circle. Between the square and the circle are four segments.
The surface area of a right prism is: +, where B is the area of the base, h the height, and P the base perimeter. The surface area of a right prism whose base is a regular n-sided polygon with side length s, and with height h, is therefore: = +.
Obtaining a better approximation to the area using finer divisions of a square and a similar argument is not simple. [10] Problem 50 of the RMP finds the area of a round field of diameter 9 khet. [10] This is solved by using the approximation that circular field of diameter 9 has the same area as a square of side 8.
Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities
The formula for the volume of a pyramidal square frustum was introduced by the ancient Egyptian mathematics in what is called the Moscow Mathematical Papyrus, written in the 13th dynasty (c. 1850 BC): = (+ +), where a and b are the base and top side lengths, and h is the height.
The lateral area, L, of a circular cylinder, which need not be a right cylinder, is more generally given by =, where e is the length of an element and p is the perimeter of a right section of the cylinder. [9] This produces the previous formula for lateral area when the cylinder is a right circular cylinder.
In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.