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Polygons and Circle – Definitions, Perimeter and Area formulas

Posted in Math Theory by Lia on 04/02/2013

Below is a table with perimeter and area formulas, for the shapes shown on the right hand side.

For a table with definitions, area and volume formulas, for the most common 3D body shapes, click here.

Shape/Description				Visual representation	Perimeter (p)	Area (A)

Polygon A closed plane figure that has three or more straight sides and angles OR *A polygon with n sides and n angles has the sum of the angles = (n-2)180˚** Examples of polygons are: Triangle (3 sides); Quadrilateral (4 sides); Pentagon (5 sides); Hexagon (6 sides); Heptagon (7 sides); Octagon (8 sides); Nonagon (9 sides); Decagon (10 sides) and so on.	Triangle A polygon with 3 sides and 3 angles The sum of the triangle’s angles is equal with 180˚	Scalene triangle A triangle with unequal sides and therefore unequal angles.	Obtuse scalene triangle A triangle with one of the angles larger than 90˚. In this case the angle A is larger than 90˚.
			Acute scalene triangle A triangle that has no angle larger than 90˚.
		Isosceles triangle A triangle that has two sides and therefore two angles equal. In this case AB = AC and angle B is equal with angle C.
		Equilateral triangle A triangle that has all sites and angles equal. In this case AB = BC =CA and angle A = angle B = angle C.
		Right triangle A triangle that has one of its angle 90˚ therefore the two adjacent sites are perpendicular on each other. In this case angle A = 90˚ and therefore AC is perpendicular on AB and reverse (AB is perpendicular on AC).
	Quadrilateral A polygon with 4 sides and 4 angles. The sum of the quadrilateral’s angles is equal with 360˚	Quadrilateral (general shape)
		Parallelogram A quadrilateral that has the opposite sides equal and the opposite angles equal. In this case AB = CD; AC = BD; angle A = angle D and angle B = angle C.
		Rhombus A parallelogram that has all sides equal.
		Rectangle A parallelogram that has all angles equal with 90°.
		Square A rectangle that has all sides equal.				$tabular{11}{11}{{A = a^2 }}$
		Trapezoid A quadrilateral with two opposite parallel sides, bases and two lateral sides, legs, that are not parallel.	Scalene trapezoid A trapezoid that has no equal sides or angles.			$tabular{11}{11}{{A = {{h({b_1} + {b_2})}/2}}}$
			Right trapezoid A trapezoid that has two adjacent angle equal with 90°. In this case angle A = angle C = 90°.
			Isosceles trapezoid A trapezoid that has equal legs and equal adjacent angle. In this case AC = BD and angle A= angle B and angle C = angle D.
	Polygon (general shape) A polygon with n sides and n angles *has the sum of the angles = (n-2)180˚** in our example therefore the sum of the angles $= (7-2)180^{circ} = 900^{circ}$ OR: There are 5 triangles inside this heptagon (a polygon with 7 sides). One triangle has the sum of its angle $180^{circ}$ therefore the polygon will have 5 times the sum of the trianle’s angles ( $= 5180^{circ} = 900^{circ}$				in our example:	(triangles that form the polygon) In our example:
Circle A closed plane curve which points are equidistant from a fixed point, the center. OR A set of points equal distanced from a point, the center.	Circle					$tabular{11}{11}{{A = {pi}{R^2}}}$ (when area is function of R) or $tabular{11}{11}{{A = {pi}{{D^2}/4}}}$ (when area is function of D)
	Circle sector A circle sector is the portion of a circle in between two radii.				where: *${}{}{}{a} = 2{pi}{R}{{alpha}/{{360}^{circ}}} =$ ${{{pi}R{alpha}}/{{180}^{circ}}}{}{}{}$ if is in degrees and,** if is in radians	*$tabular{11}{11}{{A = {pi}{R^2}{{alpha}/{{360}^{circ}}}}}$ if is in degrees and,** $tabular{11}{11}{{A = {{{R^2}{alpha}}/{2}}}}$ if is in radians
	Circle segment A circle segment is the portion of a circle in between a chord and the arc that has same end points as the chord.				where has same formula as for Circle sector and *Look here* for formula.**	$tabular{11}{10}{{A = {pi}{R^2}{{alpha}/{{360}^{circ}}} -}}$ $tabular{11}{01}{{{1/4}a{sqrt{4{R^2} -{a^2}}}}}$ if is in degrees and,* $tabular{11}{10}{{A = {{{R^2}{alpha}}/{2}} -}}$ $tabular{11}{01}{{{1/4}a{sqrt{4{R^2} -{a^2}}}}}$ if is in radians

Tagged with: geometry (2D), math theory

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