Question

A department store sells small boxes in which customers can store nails. The diagram below shows one of the boxes. The diagram is not drawn to scale. 2.54 cm, 14 cm, 8 cm. What are the lateral area and the surface area of the box to the nearest whole number? Use the large 14 cm times 8 cm rectangles on the top and bottom as the bases.

A) 112cm^2 ; 448cm^2
B) 112cm^2 ; 336cm^2
C) 56cm^2 ; 448cm^2
D) 56cm^2 ; 336cm^2

Answer 1

The answer is B) 112cm^2 ; 336cm^2.

The lateral area (LA) is the product of the perimeter (P) of the base and the height (h):
LA = Ph

P = 2l + 2w = (2 x 14) + (2 x 8) = 28 + 16 = 44 cm
LA = 44 cm x 2.54 cm = 112 cm²


The surface area (SA) is the sum of all areas:
SA = 2(lw + wh + lh)
SA = 2((14x8) + (8x2.54) + (14x2.54))
SA = 2(112 + 20.32 + 35.56)
SA = 2 * 168
SA = 336 cm²

Thus, the lateral area and the surface area are 112 cm² and 336 cm², respectively.