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What’s the area and volume formulas for a pentagonal prism?


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.

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2 Responses to “What’s the area and volume formulas for a pentagonal prism?”

  1. 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 :
    ether

  2. 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 :

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