![]() ![]() For shapes with curved boundary, calculus is usually required to compute the area. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number. A shape with an area of three square metres would have the same area as three such squares. In the International System of Units (SI), the standard unit of area is the square metre (written as m 2), which is the area of a square whose sides are one metre long. The area of a shape can be measured by comparing the shape to squares of a fixed size. Two different regions may have the same area (as in squaring the circle) by synecdoche, "area" sometimes is used to refer to the region, as in a " polygonal area". It is the two-dimensional analogue of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object. We need all the units to be cm or cm², so we need to convert 2 metres into 200 centimetres.Area is the measure of a region's size on a surface. The diagram below shows a triangular prism:Ī) Calculate the volume of the prism if l = 5 cm.ī) Calculate the volume of the prism if l = 2 m.Ī) Calculating the volume of the prism if l = 5 cm. Thus the volume of a triangular prism is 12cm 2 Volume = area of triangular cross-section × perpendicular height All lengths are the sameĬross sectional area = 1/2 × 3 × 2 cm 2 =3cm 2 That is volume of prism = Area of cross section × heightĪ) Volume = area of cross-section × perpendicular heightī) Volume = area of cross-section × perpendicular heightįind the volume of a rectangular prism whose length is 15′, it’s width is 11′ī) A cube is bounded by six square faces. If for example the cross-sectional shape was a rectangle then you just use the standard formula to calculate the area of a rectangle and multiply that by the height to find the volume. You could even have an irregular cross-sectional shape, in which case the area is often given. Hexagonal, triangular, rectangular, trapezium, isosceles, square, and almost any quadrangular shape. The cross-sectional shape of the prism can vary a lot, and could be You are therefore using cross-sectional area to find volume. The principle here is that if you can figure out the cross-sectional area (A) of the prism then it is a simple matter of multiplying that with the length (l) to find the volume (V). The surface area of the cross section multiplied by the length usually gives the volume. ![]() The volume of a prism is found by multiplying the area of its cross section by the height of the prism.Ī prism has a uniform cross section throughout the length. Recognize that the volume of a rectangular prism is the product of the lengths of its base, width, and height (V = b × w × h).Ī prism is a solid with a uniform cross – section.At the end of this lesson, student should be able to: ![]()
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