Tyrone M.

asked • 06/09/15

calculate surface area of this triangular prism

base- 7.0 cm
height- 6.1 cm
length- 5.0 cm

Scott M.

Question:
Does the 3.5 term under the square root imply that the assumption is that the triangular faces are isosceles?
IE, that the hypotenuse (and thus one side of the main body) comes from SQRT(6.12 +(7/2)2) seems to imply this. I got stuck on this since if we don't know what kind of triangle the face is, it would seem there would be an infinite number of possible surface areas.
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06/11/15

Steve C.

Oh, yes, my answer does have issues - thanks for pointing this out!  You would need to determine the length of each side of the triangle and determine the areas of the three sides separately.  One triangle side is 7 cm. (The base).  The other side lengths will depend on the angle opposite the base.  I'll need to think about this some more to see if there is just one solution...
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06/11/15

Scott M.

Thank you, I will follow with interest. I have less experience with this than you, so I am still learning but I believe there is no single solution unless it is an isosceles or right triangle. I'm not certain so please correct me if I'm wrong.
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06/12/15

Steve C.

Yes, there is no single solution to this problem.  Whoever came up with the problem, either left out a key constraint, or wanted people to struggle finding an answer.  In any case, I think we both have a better understanding about surface areas of triangular prisms.  :-)
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06/12/15

1 Expert Answer

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Steve C. answered • 06/10/15

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Steve C. Math & Chemistry Tutoring

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Assuming that "height" is the height of the triangle, the total base surface area is 2(1/2)(6.1)(7)= 42.7 cm2
Assuming the "length" is the length of the rectangular sides, one side will have the area 5(7) = 35 m2, but not enough information is given to obtain the areas of the other two sides, but limits can be determined.  If the triangle is a right triangle. The length of one leg will be 6.1 cm and the length of the other leg will be approximately 9.285 cm (√(6.12 + 72).  If the triangle is isoceles, the sides will each be approximately 7.033 cm (√(6.12 + 3.52).  The maximum lateral area will be obtained in the case of the right triangle (111.925 cm2).  The minimum lateral area will be for the case of the isoceles triangle (105.33 cm2).  So the total surface area will be somewhere between 148.03 cm2 and 154.625 cm2, depending on the measure of the angle opposite the triangle base.
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