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Prism Geometry Definition by Math Help





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Prism Geometry Definition by
Article Posted: 10/03/2012
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Articles Written: 257
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Prism Geometry Definition


 
Education
Introduction to prism geometry definition:

The definition of prisms is that they shape with two bases on two sides connected together by faces. The bases are formed of n sided polygons and the bases are connected together by the same n number of faces. The prisms where the angle between the faces and the bases is 90 degrees the prisms are called as right prisms. In this article we will see more about the prisms in detail. In geometry, a prism is a polyhedron with a n-sided polygonal base, a translated copy (not in the same plane as the first), and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases. All cross-sections parallel to the base faces are the same. Prisms are named for their base, so a prism with a pentagonal base is called a pentagonal prism. The prisms are a subclass of the prismatoids. A right prism is a prism in which the joining edges and faces are perpendicular to the base faces. This applies if the joining faces are rectangular. If the joining edges and faces are not perpendicular to the base faces, it is called an oblique prism.

More about Prism Geometry Definition:

The prisms have two bases made of n sided polygons connected by the n number of faces. So the volume of the prism will be the product of the base area and height and the total surface area will be the sum of area of the two bases and the area of the faces. This is given by,

Volume = Base Area*Height

Total surface area = 2*base area + Area of the faces.

So for a prism with n sided regular polygon of side length S and height of prism H as base the formula for calculating the volume and the total surface area is given by,

Volume = nHS2 cot (p/n)/4

Total surface area = `[{nS^2 cot (pi/n)}/2] + nSH`

Example Problems on Prism Geometry Definition:

1. Find the volume and the total surface area of a pentagonal prism with a side length of 3cm, and the height of the prism is 8cm.

Solution:

The volume of the prism = [nHS^2 cot (p/n)]/4

= [5*8*32*cot (pi/5)]/4

= [40*9*1.37)]/4

= 493.2/4

= 123.9 cm3.

Total surface area = `[[nS^2 cot (pi/n)]/2] + nSH`

= [5*32*cot (p/5)] + 5*3*8

= (45*1.37) + 120

= 61.65 + 120

= 181.65 cm2.

Practice problems on prism geometry definition:

1. Find the volume and the surface area of the hexagonal prism with a side length of 2.5cm and the height of the prism is 9cm.

Answer: Volume = 146.23 cm3 and Total surface area = 169.5 cm2.

2. Find the volume and the surface area of the octagonal prism with a side length of 3cm and the height of the prism is 7cm.

Answer: Volume = 304.36 cm3 and Total surface area = 255 cm2.

Learn more on about Nonagon Shape and its Examples. Between, if you have problem on these topics Cylinder Shape, Please share your comments.

Related Articles - Introduction to prism geometry definition, examples,

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