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Geometry and Trigonometry / Area and volume Difficulty: Hard

A right rectangular prism has a length of $28 centimeters left parenthesis cm right parenthesis$ , a width of $15 cm$ , and a height of $16 cm$ . What is the surface area, $in {cm}^{2}$ , of the right rectangular prism?

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Explanation

The correct answer is $2,216$ . The surface area of a prism is the sum of the areas of all its faces. A right rectangular prism consists of six rectangular faces, where opposite faces are congruent. It's given that this prism has a length of $28 cm$ , a width of $15 cm$ , and a height of $16 cm$ . Thus, for this prism, there are two faces with area $left parenthesis 28 right parenthesis left parenthesis 15 right parenthesis cm squared$ , two faces with area $left parenthesis 28 right parenthesis left parenthesis 16 right parenthesis cm squared$ , and two faces with area $left parenthesis 15 right parenthesis left parenthesis 16 right parenthesis cm squared$ . Therefore, the surface area, $in {cm}^{2}$ , of the right rectangular prism is $2 (28) (15) + 2 (28) (16) + 2 (15) (16)$ , or $2,216$ .