For a better explanation: Surface Area of any Prism can be found using the following formula: S.A. = 2B + Ph where B = the area of the base of your prism, P = the perimeter of the base of your prism, and h = the height(or distance between the two bases) of your prism.
In this case we have a triangular Prism so the base is in the shape of a triangle.
B = 0.5 x 3 x 8 = 12
P = 8 + 5 + 5 = 18 Note one side of the triangle has a length of 8. To find the length of the other two, we have to know a little about right triangles. The other two sides of the triangular base serve as the hypotenuse of the right triangles formed by the altitude of the triangular base(the dotted line). Furthermore the altitude cuts the side labeled 8 into two equal segments of 4. So really the altitude subdivides the triangular base into two congruent triangles each having legs of 3 and 4. Now using the Pythagorean Theorem, we can find the missing sides of the triangular base. [tex] a^{2} + b^{2} = c^{2} [/tex] is the theorem where a,b are the legs(3,4) and c is the hypotenuse(the side we are looking for) : substituting into the formula, you can solve for "c": 9 + 16 = c^2 or 25 = c^2 now just take the square root of each side and find c = 5
h = 7 the distance between the two triangles in your prism
Now lets substitute into the formula: S.A. = 2B + Ph
S.A. = 2(12) + 18(7) = 24 + 126 = 150 or 150 square centimeters since that is the unit of measure we have been given.
Let me know if you have questions..
