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# Topic: Apothem

 SparkNotes: Geometric Measurements: Area of Regular Polygons An apothem of a regular polygon is a segment with one endpoint at the center and the other endpoint at the midpoint of one of the sides. The apothem of a regular polygon is the perpendicular bisector of whichever side on which it has its endpoint. The apothem is equal to the altitude, and the perimeter is equal to the sum of the bases. www.sparknotes.com /math/geometry2/measurements/section6.rhtml   (443 words)

 Dummies::Sizing Up the Area of a Polygon Theorem 5-11: The measure of a central angle in a regular polygon is equal to 360° divided by the number of sides of the polygon. Theorem 5-12: An apothem of a regular polygon bisects the central angle (determined by the side) to which it's drawn. Theorem 5-13: An apothem of a regular polygon is a perpendicular bisector to the side it's drawn to. www.dummies.com /WileyCDA/DummiesArticle/id-1195.html   (802 words)

 Geometry: geometry Remember, the apothem is the perpendicular segment from the center to one of the sides of the pentagon. Did you notice that the apothem of the pentagon is also the radius of the circle. Since the apothem is the radius, then the radius is 8.26 units long. en.allexperts.com /q/Geometry-2060/geometry-50.htm   (468 words)

 Summary The apothem is 356 cubits with the pyramidion and 351.6 cubits without the pyramidion. But the apothem was set at 356 cubits not only to achieve a round figure, but also to indicate a relation 89/55 between the apothem and the semi-side. However, the apothem on the West side conformed, the side which conformed to the basic length at the basis, was 355.319 cubits, would indicate a minute of 1,862.398 m. www.metrum.org /key/pyramids/summary.htm   (1866 words)

 Regular Polygons Project In Section I, familiarity with the basic trigonometric functions is also required, as are their applications to computing side lengths and angles of triangles. Summary: In Section I, students derive formulas for the angles, perimeter, radius, apothem, area, median length, and diagonal lengths of a regular polygon with n sides. This segment is called the apothem, and its length is denoted by a. www.math.rutgers.edu /~erowland/polygons-project.html   (1433 words)

 London Stock Exchange - Site Search Apothem Formula, Apothem of a Polygon, In Geometry What Is Apothem, Apothem of a Regular Polygon, Length of an Apothem, Angle Bisector, Area of a Regular Polygon, Apothem Math Given a circle, the apothem is the perpendicular distance from the midpoint of a chord to the circle's center. The apothem of a regular polygon is a line... www.londonstockexchange.com /en-gb/global/H/Search?q=Apothem&rt=3&p=0   (327 words)

 Math Forum - Ask Dr. Math   (Site not responding. Last check: 2007-10-25) Date: 03/21/2001 at 18:50:40 From: Anne Hufnus Subject: Apothem of triangles I read your explanation on finding apothems for hexagons; however, it does not seem to apply to the triangle. / \ +---+-+-+---+ The apothem is that short vertical line from the center to the midpoint of an edge, and is also the apothem of the hexagon. If you look closely, you will then see that the circumradius of the triangle will be twice the apothem, since it consists of the altitudes of two of the little triangles. mathforum.org /library/drmath/view/55282.html   (206 words)

 Apothem of a Regular Polygon - Math Open Reference Definition: A line segment from the center of a regular polygon to the midpoint of a side. The apothem is also the radius of the incircle of the polygon. For a polygon of n sides, there are n possible apothems, all the same length of course. www.mathopenref.com /polygonapothem.html   (226 words)

 Poly Diameter, Radii, Pi However, if the apothem plus apothem diameter of a square is used for the diameter, and divided into the circumference of any square it gives a ratio of 4. I believe the apothem is actually the true radius of all regular polygons, and twice the apothem is the true regular polygon diameter. I dropped the traditional definitions of radius, apothem, and diameter for regular polygons and for the circle. www.theofficenet.com /~rad/Poly_Dia_Rad_PI.htm   (916 words)

 Area Polygon Calculator Apothem   (Site not responding. Last check: 2007-10-25) Calculate its perimeter, apothem, and area to the nearest tenth. Polygon Areas - This altitude is called the apothem. Dummies::Sizing Up the Area of a Polygon - Theorem 5-12: An apothem of a regular polygon bisects the central angle... www.quickcalculators.com /area-polygon-calculator-apothem.html   (848 words)

 Untitled Document The height is 280 cubits and the apothem (the slant height of the faces) is 356 cubits. All of the points along the arc in the diagram are 116 miles from Giza, 1,000 times the length of the apothem of the Great Pyramid. The length of the apothem of the Great Pyramid and the length of the sides of the triangle that inscribe the delta are also precise measures of the circumference of the earth, in relation to the precession of the equinoxes. home.hiwaay.net /~jalison/Art4.html   (1966 words)

 Geometry Message Board The apothem is the altitude to one of the congruent triangles that make up a regular polygon, using the side of the polygon and two radii (segments to the center of the polygon). Consider the right triangle formed by the apothem, half a side of the polygon, and a radius. Call the apothem a, the radius r, and half the side of the polygon x. mb.sparknotes.com /mb.epl?b=987&m=1067559&t=306907&w=1   (130 words)

 Math Forum - Ask Dr. Math   (Site not responding. Last check: 2007-10-25) Date: 6/11/96 at 0:11:46 From: RS Subject: Apothem of a hexagon I need help in finding the apothem of a regular hexagon. Date: 6/13/96 at 23:48:28 From: Doctor Brian Subject: Re: Apothem of a hexagon Well, let's divide the regular hexagon into six isosceles triangles, and then we'll deal with one of those--they're all congruent anyways, so the apothem will be the same. From here we use either the Pythagorean theorem (hypotenuse = s and one leg = s/2) or we use the 30-60-90 triangle relationship to get that the apothem is sqrt(3) * s / 2 If you've done anything with sine/cosine/tangent, then you may know that the sqrt(3) part comes from the tangent of 60. mathforum.org /library/drmath/view/54840.html   (398 words)

 Finding the Missing Sides of a Right Triangle Definition: An apothem of a regular polygon is any perpendicular line segment drawn from the center of the polygon to a side that forms a right angle with that side. Area of a regular polygon is A = ap/2 where A is the area of the polygon, a is the apothem of the polygon, and p is the perimeter of the polygon. 1) Find the area of a regular octagon whose sides have a length of 10 cm and whose apothem is 5 cm. www.scifimath.com /solutions48.htm   (144 words)

 [No title]   (Site not responding. Last check: 2007-10-25) A pentagon with an apothem 2.8 feet and a perimeter of 20.34 feet __________2. An octagon with an apothem 4.8 centimeters and a side 4 centimeters __________3. A regular hexagon with apothem 5 EMBED Equation.3   An equilateral triangle with apothem 4  A square with apothem 5 For the following regular polygons, you will follow the same steps and use the trigonometric ratios to the find some of the missing pieces. classroom.springisd.org /webs/geometry/upload/unit_15_ws_1_regular_polygons__circles.doc   (341 words)

 Re: Formulas for Hexagon -- side, apothem, radius and perimeter   (Site not responding. Last check: 2007-10-25) It appears that it must be because you seem to be assuming that all sides are congruent. what is the apothem of a regular dodecagon with side length of 6 mary 16:53:27 05/19/02 ( : (1) radius: s = 2(r)sin(30), : (2) apothem: s = 2(a)tan(30), and : (3) perimeter: s = p/8, :...where s, r, a, and p represent length of side, radius, apothem and perimeter, respectively. www.mathguide.com /bbs/Messages2002/1339.html   (307 words)

 US Datamines : Support A: An apothem is the distance from the center of a square, perpendicular to the edge of a square. When you order census data by ZCTA ZIP code and apothem, this apothem would be the distance from the ZCTA ZIP code to the edge of the square. In contrast, USPS ZIP codes serve addresses with no correlation to census block boundaries; therefore, the area covered by a ZCTA may include mailing addresses associated with ZIP codes that are not the same as the ZCTA. www.usdatamines.com /support.html   (186 words)

 apothem - OneLook Dictionary Search Tip: Click on the first link on a line below to go directly to a page where "apothem" is defined. apothem : The American Heritage® Dictionary of the English Language [home, info] Apothem : Online Plain Text English Dictionary [home, info] www.onelook.com /?w=apothem   (195 words)

 Regular polygon area formula - Math Open Reference If you know the apothem, or inradius, (the perpendicular distance from center to a side. A is the length of the apothem (inradius) If you know the apothem (the perpendicular distance from center to a side. www.mathopenref.com /polygonregulararea.html   (270 words)

 Circle Formulas   (Site not responding. Last check: 2007-10-25) Segment Height ED = Radius AO - Apothem OE 2) Radius AO & Chord AB From the Pythagorean Theorem OE² = AO² - AE² Apothem OE = Radius AO - Segment Height ED Angle AOE = arc tangent (AE/OE) 6) Chord AB & Apothem OE From the Pythagorean Theorem www.1728.com /circpart.htm   (373 words)

 The area of a regular decagon Question: how do i find the area of a regular decagon with sides of length 6 cm and an apothem of 9.2 cm? If you know the length of the apothem and the side length, then you can construct two identical right triangles for each side. Since the apothem always bisects the side, you know the height and width of the triangles and can calculate the area, multiply by the number of triangles and get your answer. mathcentral.uregina.ca /QQ/database/QQ.02.06/ester1.html   (93 words)

 Proof1.htm   (Site not responding. Last check: 2007-10-25) The apothem of a square is the segment from the center to a midpoint of one of its sides. So by drawing this square with its radius and apothem we can use our concepts of 45-45-90 triangles to solve for their lengths. Square root both sides to find A which is the apothem length. web.pdx.edu /~spinto/Proof1.htm   (352 words)

 Golden spiral The phi ratio is found in the architecture of the Great Pyramid in the triangle formed by the height, half-base, and the apothem, or diagonal. If the half - base is given a value of 1, this gives the value of phi for the apothem, and the square root of phi for the height. The Golden Section shows up again and again in Giza and in much more baffling and tedious ways (Entire volumes have been written on the geometries involved in the pyramids construction). www.ka-gold-jewelry.com /p-articles/golden-spiral.php   (622 words)

 Polygon - Wikipedia, the free encyclopedia Several formulae give the area of a regular polygon: half the perimeter multiplied by the length of the apothem (the line drawn from the centre of the polygon perpendicular to a side) The area A of a simple polygon can be computed if the cartesian coordinates (x en.wikipedia.org /wiki/Apothem   (745 words)

 math notebook We draw a regular hexagon, or any regular polygon, and draw in all of its radii, thus breaking it up into congruent triangles. We draw in the apothem of each triangle, and using our formula for the area of triangles we find that its area is one half apothem times perimeter, where the perimeter is the sum of its sides: If the sides of a regular polygon are increased indefinitely, the apothem becomes the radius of a circle, and the perimeter becomes the circumference of a circle. mysite.verizon.net /res8ydyw/id7.html   (974 words)

 Quandaries & Queries at Math Central how do i find the apothem and area of a decagon that has a perimeter of 60? if the area of a regular hexagon is 259.807 how do i find the length of each side, and the apothem? find the area of a regular hexagon with a apothem of 9 mathcentral.uregina.ca /QandQ/topics/apothem   (97 words)

 Re: apothem, radius and side of polygons   (Site not responding. Last check: 2007-10-25) In Reply to: finding the apothem and radius with only the side& # of polygons given posted by Zach Norling on October 04, 2002 at 08:28:26: "I'm currently working with regular polygons and need to figure out the apothem and radius with only the side and # of sides given. : Zach, you wrote: : "I'm currently working with regular polygons and need to figure out the apothem and radius with only the side and # of sides given. www.mathguide.com /bbs/Messages2002/2630.html   (171 words)

 Encyclopedia Galctica   (Site not responding. Last check: 2007-10-25) We draw a regular hexagon, or any regular polygon, and draw in all of its radii, thus breaking it up into congruent triangles. We draw in the apothem of each triangle, and using our formula for the area of triangles we find that its area is one half apothem times perimeter, where the perimeter is the sum of its sides: If the sides of a regular polygon are increased indefinitely, the apothem becomes the radius of a circle, and the perimeter becomes the circumference of a circle. www.project-genesis.org /id2.html   (1246 words)

 index   (Site not responding. Last check: 2007-10-25) Apothem Capital Management LLC ("ACM") specializes in computerized trading of the equity and futures markets. The investment objective of our trading programs is stable but moderate capital appreciation. Michael Tan, PhD, CFA Apothem Capital Management LLC www.apothemcapital.com   (88 words)

 Apothem   (Site not responding. Last check: 2007-10-25) With a few pitch adjustments (octave displacements), most of the other combinations are still possible although it probably works best with all wind instruments. The title 'Apothem' refers to the slant height of a pyramid, specifically the Great Pyramid of Khufu, a longtime preoccupation of mine. The musical lines represent a sloping world, sometimes gliding over the slanting surfaces and sometimes giving glimpses of greater depths beneath the surface. www.sibeliusmusic.com /cgi-bin/show_score.pl?scoreid=68777   (206 words)

 TribalWar Forums - calling apothem apothem its been so long i had to sit and think to try and remember your name : If this problem persists, please contact the webmaster of this site. apothem was tw's #1 poster for two consecutive terms before all coolness disappeared from tw and the award was retired www.tribalwar.com /forums/showthread.php?threadid=186699   (148 words)

 www.ElvenKids.com - a website by kids for kids SUM OF THE PERIMETERS, GIVEN LATERAL AREA AND APOTHEM SUM OF THE RADIUSES, GIVEN LATERAL AREA AND APOTHEM RADIUS, GIVEN AREA AND HEIGHT OF THE SPHERICAL CAP www.elvenkids.com /tools/geometria/Geometria.php   (825 words)

 TribalWar Forums - calling apothem TribalWar Forums > TribalWar > General Discussion > calling apothem 01-29-2003, 11:56 PM apothem its been so long i had to sit and think to try and remember your name : 01-30-2003, 12:22 AM apothem was tw's #1 poster for two consecutive terms before all coolness disappeared from tw and the award was retired www.tribalwar.com /forums/archive/index.php/t-186699.html   (185 words)

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