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Geometry and Trigonometry / Area and volume Difficulty: Medium

The length of each edge of a box is $29$ inches. Each side of the box is in the shape of a square. The box does not have a lid. What is the exterior surface area, in square inches, of this box without a lid?

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Explanation

The correct answer is $4,205$ . The exterior surface area of a figure is the sum of the areas of all its faces. It's given that the box does not have a lid and that each side of the box is in the shape of a square. Therefore, the box consists of $5$ congruent square faces. It's also given that the length of each edge is $29$ inches. Let $s$ represent the length of an edge of a square. It follows that the area of a square is equal to $s^{2}$ . Therefore, the area of each of the $5$ square faces is equal to $29 squared$ , or $841$ , square inches. Since the box consists of $5$ congruent square faces, it follows that the sum of the areas of all its faces, or the exterior surface area of this box without a lid, is $5 left parenthesis 841 right parenthesis$ , or $4,205$ , square inches.