Jon G. answered • 02/28/13

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Patient knowledgeable STEM educator/former healthcare practitioner

Sorry for the extremely long reply, however, you don't provide enough information to begin to answer this question. Ten what? the sides length of the sides, the height of the triangle ends, ten what. I'm assuming you mean the sides(s) of the prism are square, which means the total surface area of the sides are s(squared) times 3, since there are 3 sides to the prism. This then leads to the triangle ends being equilateral triangles, all 3 sides are equal lenghth. To calculate the area of 1 triangle, the height of the triangle needs to be calculated. Since all the sides of the rectangles are equal(s), one side would be the hypotenuse and 1/2 (s) which is one leg of the triangle, creating a right triangle, and using the Pythagoean Theorem, calculate the other leg(l), which is the height. The area of ONE triangle end would be (s) times (l), multiply that times 2 would give you the area of both ends. However, this is how one would begin to answer this kind of problem. A prism is constructed of 3 rectangles, the sides, and 2 triangles, the ends. The lengths and widths of the prism help calculate the area of the sides, so l x w = surface area of one side, multiply times 3 will give you the total surface area of the sides. The dimensions of the ends, the triangles, side lengths, and/or height of the triangles can also be the dimensions of the rectangle. I know its getting confusing, the best way to envision this is to draw the prism and label the sides. Find the area of the triangles, 1/2 b x h is the area of 1 triangle, multiple times 2 to get the area of both triangles. Add the two products, total area of the rectangles and the area of the 2 triangles and that will equal the total surface area of the prism. The dimensions of the prism angles of the triangles can make calculating the total surface area simple or complicated because the height of the triangle can differ from the dimensions of the rectangle and using the Pythagorean Theorem a(squared) + b(squared) = c(squared) might be need to calculated the height, if the triangles aren't right triangles. But the areas of the rectangles is a constant, because by definition, a prism is a polygonal figure composed of 3 rectangles sides and 2 triangle sides. I hope this answers your question, or at least heads you in the correct direction, but again, your question..."find the told(total) suface(surfacce) area of a square prism is ten. Good luck...again, the best way is to draw the figure.