Comments on: What’s the area and volume formulas for a pentagonal prism? http://www.thearealist.com/area-formulas/whats-the-area-and-volume-formulas-for-a-pentagonal-prism Fri, 03 Feb 2012 13:07:59 -0500 http://wordpress.org/?v=2.8.4 hourly 1 By: Geezah http://www.thearealist.com/area-formulas/whats-the-area-and-volume-formulas-for-a-pentagonal-prism/comment-page-1#comment-1531 Geezah Tue, 15 Dec 2009 06:51:59 +0000 http://www.thearealist.com/area-formulas/whats-the-area-and-volume-formulas-for-a-pentagonal-prism#comment-1531 Like any prism, the volume is the area of the base times the height. If the base is a REGULAR pentagon with side length "s", then you can slice it up into 5 isoceles triangles with angle 360/5 = 72 and base length 5. Each of these triangles has a height of s*cot(36), so the total area of the pentagon is 5*(1/2)*s*(s*cot(36)) = (5s²/2)cot(36) = (s²/4)√(25 + 10√5). So if h is the height, then the volume is (s²h/4)√(25 + 10√5) The surface area would just be the area of the top plus the bottom and 5 sides. Then the area of the five surrounding rectangular sides of the prism is 5sh. Adding these to the top and bottom, you get 5sh + (s²/2)√(25 + 10√5).<br><b>References : </b><br> Like any prism, the volume is the area of the base times the height. If the base is a REGULAR pentagon with side length "s", then you can slice it up into 5 isoceles triangles with angle 360/5 = 72 and base length 5. Each of these triangles has a height of s*cot(36), so the total area of the pentagon is 5*(1/2)*s*(s*cot(36)) = (5s²/2)cot(36) = (s²/4)√(25 + 10√5). So if h is the height, then the volume is
(s²h/4)√(25 + 10√5)

The surface area would just be the area of the top plus the bottom and 5 sides. Then the area of the five surrounding rectangular sides of the prism is 5sh. Adding these to the top and bottom, you get 5sh + (s²/2)√(25 + 10√5).
References :

]]> By: Thin Kaboudit http://www.thearealist.com/area-formulas/whats-the-area-and-volume-formulas-for-a-pentagonal-prism/comment-page-1#comment-1530 Thin Kaboudit Tue, 15 Dec 2009 06:36:59 +0000 http://www.thearealist.com/area-formulas/whats-the-area-and-volume-formulas-for-a-pentagonal-prism#comment-1530 The area of a regular pentagon is equal to 1.720a (where a= the length of a side), so multiply that by length for volume of a regular prism, or for area, multiply it by 2 and add (5 times [a * L]), where L is the length. In the case of an irregular pentagonal prism, divide one end into 5 triangles, find the area of each, & add them together, then follow the same steps as above.<br><b>References : </b><br>ether The area of a regular pentagon is equal to 1.720a (where a= the length of a side), so multiply that by length for volume of a regular prism, or for area, multiply it by 2 and add (5 times [a * L]), where L is the length.

In the case of an irregular pentagonal prism, divide one end into 5 triangles, find the area of each, & add them together, then follow the same steps as above.
References :
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