GMAT Math : Calculating the surface area of a prism
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Example Questions
Example Question #11 : Prisms
The length of a rectangular prism is twice its width and five times its height. If 
If we let 
Since the length is five times the height, the height is one fifth the length, so 
The surface area of a rectangular solid is
which can be rewritten as
Example Question #12 : Prisms
Each base of a right prism is a regular hexagon with sidelength 6. Its height is two thirds the perimeter of a base. Give the surface area of the prism.
The perimeter of a regular hexagon with sidelength 6 is
The height of the prism is two thirds of this, so
The lateral area of the prism is the product of the perimeter of a base and the height of the prism, so
The area of each base can be calculated using the area formula for a regular hexagon:
The surface area is the sum of the lateral area and the areas of the bases:
Example Question #13 : Prisms
Refer to the above diagram. The perimeter of 
Insufficient information is given to answer the question.
Since each side of 
Each square side, therefore, has diagonal 10, and, by the 45-45-90 Theorem, each side of each square - and each edge of the cube - measures 
Example Question #14 : Prisms
A right prism has as its bases two triangles, each of which has a hypotenuse of length 25 and a leg of length 7. The height of the prism is one fourth the perimeter of a base. Give the surface area of the prism.
The second leg of a right triangle with hypotenuse of length 25 and one leg of length 7 has length
The area of this right triangle is half the product of the lengths of the legs, which is
The perimeter of each base is
and the height is one fourth this, or
The lateral area of the prism is the product of its height and the perimeter of a base; this is
The surface area is the sum of the lateral area and the two bases:
Example Question #15 : Prisms
The length of a cube is increased by 20%, and the width is decreased by 20%. Which of the following must happen to the height so that the resulting rectangular prism will have the same surface area as the original cube?
The height must be increased by 4%.
The height must remain the same.
The height must be decreased by 4%.
The height must be decreased by 2%.
The height must be increased by 2%.
The height must be increased by 2%.
To look at this more easily, assume the cube has sides of length 100; this argument generalizes to any size. The surface area of the cube is
After the changes, the resulting rectangular prism will have length
and width
The surface area of a rectangular prism is
This means that the height of the prism must be 102% of the height of the cube - equivalently, the height must be increased by 2%.
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