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# how to find height in a triangular prism

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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.

From Yahoo Answers

Question:This triangular prism is irregular. The height is 2 cm. One side is 10 cm, second side is 6cm and the third side is 8cm. It has a 90 degrees angle. How to find it's area?

Answers:Figure each side separately. Figure the base separately. add them together. Since there is a 90 angle, the base must be a Right angle. A of Right angle is bh 2 Sides appear to be scalene angles. So, side side Base: (10cm 6 cm) / 2 = 30cm Sides: (10cm 2cm)/2 = 10cm ...........,(6cm 2cm)/2 = 6cm ............(8cm 2cm)/2 = 8cm 30+10+6+8 = 54cm

Question:So there is a big triangular prism & a small one. The height of the big one is 8 yd & the small one 4 yd. Nothing else is given except the big prism's volume, which is 88 yd. How can I find the volume of the small prism? They are also proportional!

Answers:letters in UPPER CASE are variables set for the BIG prism, while letters in LOWER CASE are variables set for the SMALL prism. volume of triangular prism = 1/3 * area of the base * height = 1/3 (1/2 ab) * height set ab as a constant K volume = 1/6 *K*height V=88; H=8 substituting, 88=1/6 * K * 8 K = 66 (sub this to get the small prism's vol) v=1/6 * 66 * 4 v=44

Question:how do you find the surface area of a triangular prism? Triangle Base 6cm, triangle height 5.2cm, prism height 16cm. Please show how you solved! Thanks! can you give me the formula also thanks!

Answers:Triangular prism surface area = = 2 times area of a triangular end + end perimeter x prism height Area of the two ends = = 2 x 0.5 x base x height = 2 x 0.5 x 6 x 5.5 = 33 sq cms Perimeter of (isosceles) triangular end = = 2 times sloping side + triangle base Length of a sloping side = = Square root of (3^2 + 5.5^2) = Square root of 39.5 = 6.285 cm therefore: perimeter of triangular end = = 6.285 + 6.285 + 6 = 18.57 cm Area of prism sides = = perimeter x height = = 18.57 x 16 = 297.12 sq cm Total surface area of prism = = 33 + 297.12 = 330.12 sq cm

Question:Ok there is a triangular prism that has a surface area of 100cm squared... how wud i make an exact 3-D triangular prism?? the triangle has to be a right triangle, i need to know all the lengths and stuff like that i need just one way to make one out of paper

Answers:There are an infinite number of such. The larger the ends, the shorter the length. For example, if the triangle was 5 by 5 by 5* 2 then the length = 75/(5+5+5* 2) = 4.39334 cm