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# right triangular prism volume formula

From Wikipedia

Triangular prism

In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.

Equivalently, it is a pentahedron of which two faces are parallel, while the surface normals of the other three are in the same plane (which is not necessarily parallel to the base planes). These three faces are parallelograms. All cross-sections parallel to the base faces are the same triangle.

A right triangular prism is semiregular if the base faces are equilateral triangles, and the other three faces are squares.

The dual of a triangular prism is a 3-sided bipyramid.

The symmetry group of a right 3-sided prism with triangular base is D3h of order 12. The rotation group is D3of order 6.

The symmetry group does not contain inversion.

It can be considered as a truncatedtrigonal hosohedron.

## Volume

The volume of any prism is the product of the area of the base and the distance between the two bases. In this case the base is a triangle so we simply need to compute the area of the triangle and multiply this by the length of the prism:

V = \frac{1}{2} bhl where b is the triangle base length, h is the triangle height, and l is the length between the triangles.

## Related polyhedra

It is related to the following sequence of uniform truncated polyhedra.

Question:Is it the same as a regular triangle?

Answers:Yes....there are a few versions. But basically, it is l x w x h / 2

Question:I am having trouble with this problem, I don't quite understand it. If you could help, it would be great. The problem is: Find the volume of a right triangular prism whose base is an isosceles right triangle with a hypotenuse of 10cm and whose height is 23 cm. Any and all help is appreciated. :] Please and Thank you very much.

Answers:Well, since the base is an isosceles right triangle, this tells you that the sides are 10 cm, 23 cm, and 23 cm. Knowing that, you can find the area of the base, using the formula for area of a triangle (1/2 bh). Then, you multiply the base times the height of the entire triangular prism, which gives you the volume.

Question:http://www.flickr.com/photos/23761267@N02/4265299847/ a. 630 cm^3 b. 90 cm^3 c. 420 cm^3 d. 1,260 cm^3

Answers:The volume of a prism is: V = [Area of the Base] * [height] The area of the right triangular base is (1/2) b h V = 90 * 7 = 630 cm^3 QED

Question:I have an official exam on this monday coming and I really want to know what the volume of a triangular prism is. Is it length*width*height or cross section*base or something different. Please only answer if u r totally sure about it thanks.

Answers:It is area of the cross section times the length in actual fact. So in this case it would be area of the triangle times the length given. I am 100% sure that with Edexcel papers they have a formula sheet with the formula for this given. Oh but they don't give every single formula you need to know. Just a few. Good luck!