Question 248347
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The Surface Area of ANY prism is simply the sum of the areas of all of the surfaces of the prism.  A triangular prism has 2 bases and three faces.  If it is a right triangular prism, then the total surface area of the 3 faces is the perimeter of the base times the height.  The area of one of the bases is just one of the sides times its associated triangle altitude divided by 2.  But since you need the area of two bases, just base times altitude gives you the area of both bases.


In sum, for any right prism (no matter what the shape of the base is):


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ SA\ =\ 2\,\cdot\,B\ +\ P\,\cdot\,h]


Where *[tex \LARGE B] is the area of a base, *[tex \LARGE P] is the perimeter of a base, and *[tex \LARGE h] is the height of the prism.


For a triangular prism the above is equivalent to:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ SA\ =\ bh_b\ +\ P\,\cdot\,h]


where *[tex \LARGE b] is the measure of the base of the base triangle and *[tex \LARGE h_b] is the altitude of the base triangle.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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