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Plane Geometry FormulasPlane Geometry Formulas "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #2 20060402 23:37:15
Re: Plane Geometry FormulasTriangle: where b is the base and h is the height or the altitude. If the lengths of the three sides of a triangle are known, the area can be calculated using Hero's formula. where a,b,c are the three sides of the triangle and s is the semiperimeter, If the three sides of the triangle are equal, the triangle is called an equilateral triangle and each angle is 60 degrees. The area of an equilateral triangle is given by the formula where a is the length of each side. The altitude or height, h, of an equilateral triangle is and the perimeter is . Square: A square consists of four equal sides and each side is perpendicular to the other, and opposite sides are parallel. If a is the length of the side of a square, the are A is Perimeter = 4a Length of the diagonal is equal to Rectangle. A rectangle is a quadrilateral with opposite sides parallel to each other and each side perpendicular to the adjacent side. The opposite sides are equal. Area = l x b (where l and b are the sides) Perimeter = 2(l+b) Length of the diagonal = Character is who you are when no one is looking. #3 20060404 01:28:42
Re: Plane Geometry FormulasCircle where r is the radius. Circumference of a circle = Area of a semicircle = Character is who you are when no one is looking. #4 20060404 01:40:59
Re: Plane Geometry FormulasParallelogram There is also a formula for the area of a trapezoid, where the length of all sides are known:
Last edited by Patrick (20060404 01:42:02) #5 20060408 16:01:16
Re: Plane Geometry FormulasRegular Polygons in degrees. Sum of all the exterior angles = 360° No. of sides = 360°/Exterior angle. where n=no. of sides and s=length of each side. Perimeter = n x s No. of diagonals = Character is who you are when no one is looking. #6 20060408 16:46:18
Re: Plane Geometry FormulasQuadrilateral where a=length of a side. Character is who you are when no one is looking. #7 20060408 20:42:24
Re: Plane Geometry FormulasCircle (cont'd) where r is the radius and θ is the angle made by the two radii. Sector of a circle is the area of a circle between two radii. Area of a sector of a circle. where l is the length of the arc. Segment: A sector minus the triangle formed by the two radii is called the segment. Area of the segment, Perimeter of the segment : Length of the arc + length of the chord Character is who you are when no one is looking. #8 20060806 11:44:23
Re: Plane Geometry FormulasCircle Inscribed in a Triangle where the semiperimeter s of the triangle is given by Circle Circumscribing a Triangle The radius of a circle circumscribing a triangle of sides a, b, and c is given by where once again s is the semiperimeter of the triangle. Regular ngon Inscribed in a Circle The area of a regular ngon inscribed in a circle of radius r is given by The perimeter of the ngon is given by Regular ngon Circumscribing a Circle The area of a regular ngon circumscribing a circle of radius r is given by The perimeter of the ngon is given by Ellipse The area of an ellipse of semimajor axis a and semiminor axis b is given by The perimeter of the ellipse is given by or approximately #9 20070812 20:40:27
Re: Plane Geometry FormulasArea of a regular ngon if the side length is known Where n is the number of sides of the ngon, and s is the side length. Area of a regular ngon if the diagonal length is known (formulated myself ): Where n is the number of sides of the ngon and R is the length of a diagonal. (Oh I see ganesh has the first formula in a different form) Last edited by Identity (20070813 02:51:21) #10 20090114 22:50:15
Re: Plane Geometry FormulasRhombus: where are the two diagonals. The perimeter, P, is given by the formula Character is who you are when no one is looking. #11 20090114 23:01:37
Re: Plane Geometry FormulasRing: where R is the radius of the outer circle and r is the radius of the inner circle. Character is who you are when no one is looking. #12 20090115 02:49:03
Re: Plane Geometry Formulas
This is wrong! It is #13 20090115 02:53:05
Re: Plane Geometry FormulasMore Rhombus properties: Let be a nonobtuse interior angle of a rhombus with side and diagonals and . Then (i) If you fix and vary , the sum of the squares of the diagonals is constant. Indeed . (ii) If you fix and vary , the ratio of the diagonals is constant. Indeed . #14 20090115 17:29:12
Re: Plane Geometry FormulasJaneFairfax, Character is who you are when no one is looking. #15 20090313 17:16:05
Re: Plane Geometry FormulasCircumscribed Circle where Δ is the area of the triangle. Inscribed Circle A circle which touches the three sides of a triangle a, b, and c internally is called an inscribed circle or incircle. The centerof this circleis called the incenter and the radius of the circle is called the inradius. If r be the radius, then . . Radii of Inscribed and Circumscribed Circles The radius of the inscribed circle r of a regular polygon is given by The Radius of a circumscribed circle of a regular polygon is given by . Area of a Regular Polygon Character is who you are when no one is looking. 