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.
3.12 cm
5 cm
17 cm
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)
• 69 cm^: 307 cm=
• 69 cm?: 392 cm=
137 cm*;
307 cm₴
137 cm₴: 392 cm?
The lateral area of the box can be found by finding the perimeter of the top and bottom bases and multiplying it by the height of the box.
Perimeter of the top base = 17 cm + 5 cm + 17 cm + 5 cm = 44 cm
Lateral area = Perimeter of the top base * height = 44 cm * 3.12 cm = 137.28 cm² ≈ 137 cm²
The surface area of the box can be found by adding the area of the top base, bottom base, and the lateral area.
Area of the top base = 17 cm * 5 cm = 85 cm²
Surface area = 2 * (Area of the top base) + Lateral area = 2 * 85 cm² + 137 cm² = 307 cm² ≈ 307 cm²