Question 575432: what is the surface area and volume of a right triangular prism with sides of six eight ten and a height of nine inches
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! If the triangular base of the prism has sides of length six, eight and ten inches, it is a right triangle, because all triangles with side lengths in the ratio 3:4:5 are right triangles.
Side lengths of 3, 4, and 5 satisfy Pythagoras relationship:
 so a triangle with sides of those lengths is a right triangle. Triangles with the same side lengths ratios are similar and therefore are also right triangles.
The surface area of the base, in square inches, is
 because the right triangle's legs, measuring 6 and 8 inches, are perpendicular, and can be taken as base and height of the triangle.
The perimeter of the base, in inches, is
 , so the lateral area (perimeter of base times height), in square inches, is
Then, the total surface area (the lateral area plus the areas of the two bases), in square inches, is
The volume of a prism is the surface of the base times the height, so the volume of the prism in the problem, in cubic inches, is
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