A jewelry store buys small boxes in which to wrap items that it sells. The diagram below shows one of the boxes. Find the surface area of the box to the nearest whole number.
1.66 cm
14 cm
7 cm
There are six faces to this box, each with its own surface area.
The top and bottom faces are both squares with side length 7 cm, so their surface areas are each (7 cm)^2 = 49 cm^2.
The four side faces are all rectangles with one side length of 7 cm and the other side length equal to the sum of the other two side lengths. Since those two side lengths are each 1.66 cm, the total length of each side face is 7 cm + 1.66 cm + 1.66 cm = 10.32 cm. So the surface area of each side face is (7 cm) x (10.32 cm) = 72.24 cm^2.
To find the total surface area, we add up the surface areas of all six faces:
2(top/bottom) + 4(sides) = 2(49 cm^2) + 4(72.24 cm^2) = 296.96 cm^2
Rounding to the nearest whole number, the surface area of the box is 297 cm^2.