30 JULY 2021

AREASURFACE AREA

FLOOR AREA

CARPET AREA

COMMON ACRONYMS

A, SQM, SFT, GLA, GFA, BUA

COMMON STANDARDS OF PRACTICE

- V. Garga, R. Townsend, and D. Hansen, "A Method for Determining the Surface Area of Quarried Rocks," Geotechnical Testing Journal 14, no. 1 (1991): 35-45.
- General Conference on Weights and Measures, The International Bureau of Weights and Measures

DEFINITION

WHY

Area is a measure of how much space there is inside a shape or on the surface of a body. Perimeter and area are two important and fundamental mathematical topics. They help to quantify physical space and also provide a foundation for more advanced mathematics found in algebra, trigonometry, and calculus.

WHEN

Calculating the area of a shape or surface is useful in everyday life; for example to calculate how much paint should be purchased to cover a wall, how many tiles should be purchased to finish a floor, how much grass seed you need to sow a lawn, much cloth to buy to stich a curtian, or how much rent to pay for an apartment.

HOW

Common formula for calculating areas of polygons are give below;

- Circle: A = π r²

where "r" is the radius of circle and "π" is the ratio of the circumference of any circle to the diameter of that circle and equals 3.14159265359 - Triangle: A = ½ B h = √ (s [(s-a) (s-b) (s-c)]

where "B" is the length of the base, and "h" is the length of the altitude of the triangle. In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex). The length of the altitude, often simply called "the altitude", is the distance between the extended base and the vertex. There are many more ways/ formulae to find the area of a triangle depending on how much information is available about the angles and/or lengths of sides. In the second formula known as heron's formula, "s" is the semi-perimter of the triangle which equals to (a + b + c)/2, and "a", "b", and "c" are the lengths of 3 sides of the triangle. - Square: A = s²

where "s" is the length of one of the sides - Rectangle: A = l w

where "l" is the length (or height) of the rectangle and "w" is the width (or breadth) of the rectangle. - Parallelogram: A = B h

where where "B" is the length of the base and "h" is the length of the altitude of the parallelogram. The area of a parallelogram is the sum of two triangles of equal area. - Ellipse: A = π x y

where "x" is the semi-major axis (major semiaxis) or the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. "y" is the semi-minor axis (minor semiaxis) of an ellipse that is at right angles with the semi-major axis and runs to the perimeter. "π" is the ratio of the circumference of any circle to the diameter of that circle and equals 3.14159265359 - Curve: A = ∫
^{a}_{b}f(x) dx

where "A" is the area between a positive-valued curve and the horizontal axis, measured between two values "a" and "b" (b is defined as the larger of the two values) on the horizontal axis, and "f(x)" is the function that represents the curve.

- Sphere: A = 4 π r
^{2}= π d^{2}

where "r" is the radius and "d" is the diameter - Cube: A = 6 s
^{2}

where "s" is the side of the cube - Cuboid: A = 2 (l w + l h + w h)

where "l" is the length, "h" is the height, and "w" is the width. - Prism: A = 2 B + P h

where "B" is the area of one base, "P" is the perimeter of one base, "h" is the height - Cylinder (closed): A = 2 π r
^{2}+ 2 π r h = 2 π r (r + h)

where "r" is the radius of the circular base, h is the height of the cylinder - Pyramid: A = B + (P L / 2)

where "B"is the area of base, "P" is the perimeter of base, "L" is the slant height

EXAMPLES

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