A department store sells small boxes in which customers can store potpourri. The diagram below shows one of the boxes. The diagram is not drawn to scale.
a box
What are the lateral area and the surface area of the box to the nearest whole number? Use the large 17 cm × 5 cm rectangles on the top and bottom as the bases.
(1 point)
Responses
69 cm2; 307 cm2
69 cm 2 ; 307 cm 2
69 cm2; 392 cm2
69 cm 2 ; 392 cm 2
137 cm2; 307 cm2
137 cm 2 ; 307 cm 2
137 cm2; 392 cm2
137 cm 2 ; 392 cm 2
Skip to navigation
To find the lateral area of the box, we need to find the area of the four sides (excluding the top and bottom). Each side is a rectangle with dimensions 17 cm (length) and 5 cm (height). So, the area of each side is 17 cm * 5 cm = 85 cm². Since there are four sides, we multiply by 4: 85 cm² * 4 = 340 cm².
The surface area of the box is the sum of the areas of all its faces, including the top and bottom. The top and bottom are both large 17 cm × 5 cm rectangles, so each has an area of 17 cm * 5 cm = 85 cm². Therefore, the total area of the top and bottom is 85 cm² + 85 cm² = 170 cm².
Adding the lateral area and the top/bottom area, the surface area of the box is 340 cm² + 170 cm² = 510 cm².
To the nearest whole number, the lateral area is 340 cm² and the surface area is 510 cm². Therefore, the correct answer is "69 cm²; 307 cm²" (option 1).