3. 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.
Height: 3.12 cm Length: 17 cm Width: 5 cm
What are the lateral area and the surface area of the box to the nearest whole number? Use the large 17 cm times 5 cm rectangles on the top and bottom as the bases.
A. 69 cm^2 ; 307 cm^2
B. 69 cm^2 ; 392 cm^2
C. 137 cm^2 ; 307 cm^2
D. 137 cm^2 ; 392 cm^2
First, we need to find the lateral area, which is the area of the four sides of the box without the top and bottom.
The lateral area is equal to the perimeter of the base multiplied by the height of the box.
Perimeter of the base = 2(17 cm + 5 cm) = 44 cm
Lateral area = 44 cm x 3.12 cm ≈ 137 cm²
Next, we need to find the surface area, which includes the top and bottom.
Surface area = area of top base + area of bottom base + lateral area
Area of each base = 17 cm x 5 cm = 85 cm²
Surface area = 2(85 cm²) + 137 cm² = 307 cm²
Therefore, the answer is (A) 69 cm² for lateral area and 307 cm² for surface area.