Formulas for Various Areas

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Formulas for Various Areas

The abbreviations used are: b = base (length of any side of a plane figure); a = altitude (perpendicular distance from the farthest point of the figure to the extended base); s = side; r = radius (of the base circle in the case of the cylinder or cone); l = slant height (distance from vertex to base of a cone measured on its surface).


Plane Figures	Area

triangle	ab /2
parallelogram	ab
rectangle	ab
square	s²
circle	π r²


Solids	Total Surface Area

right circular cylinder	2π r ( r + a )
right circular cone	π r ( r + l )
sphere	4π r²

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area

area measure of the size of a surface region, usually expressed in units that are the square of linear units, e.g., square feet or square meters. In elementary geometry, formulas for the areas of the simple plane figures and the surface areas of simple solids are derived from the linear dimensions of these figures. Examples are given in the table entitled Formulas for Various Areas . The areas of irregular figures, plane or solid, can be computed or closely approximated by the use of integral calculus .

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