The surface area of a rectangular prism given is 126 sq in. What is the height of the prism?

5 in

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4 in

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8 in

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6 in

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Solution

The correct option is D $6 in$

Let h be the height of the rectangle.

Area of rectangular face $A o r C = L e n g t h \times W i d t h$
$= 5 i n \times h i n = 5 h s q i n$

Area of rectangular face $B o r D = L e n g t h \times W i d t h$
$= 3 i n \times h i n = 3 h s q i n$

Area of rectangular face $E o r F = L e n g t h \times W i d t h$
$= 3 i n \times 5 i n = 15 s q i n$

Surface area of rectangular prism = Area of rectangular face A + Area of rectangular face B + Area of rectangular face C + Area of rectangular face D + Area of rectangular face E + Area of rectangular face F
$= 5 h s q i n + 3 h s q i n + 5 h s q i n + 3 h s q i n + 15 s q i n + 15 s q i n$
$= 16 h s q i n + 30 s q i n$
$= 126 s q i n$
$16 h s q i n = 126 - 30 s q i n = 96 s q i n$
$h = 96 \div 18 = 6 i n$

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