Question

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, 17 cm, 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.
* 69 cm2; 307 cm2
* 69 cm2; 392 cm2
* 137 cm2; 307 cm2
* 137 cm2; 392 cm2

Answer 1

The lateral area is expressed as the product of the perimeter of the base and the height. While the surface area is the sum of all areas. The lateral area and the surface area of the box is calculated as follows:

LA = Ph 
P = 2l + 2w = (2 x 17) + (2 x 5) = 44 cm
LA = 44 cm x 3.12 cm = 137.28 cm

SA = 2(lw + wh + lh)
SA = 2[(17x5) + (5x3.12) + (17x3.12)]
SA = 307.28 cm

Thus, the lateral area and the surface area are 137 cm and 307 cm, respectively.