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.
There are six faces to this box: a rectangular top and bottom and four trapezoidal sides.
To find the surface area, we need to calculate the area of each face and then add them up.
Area of top and bottom:
Length = 5 cm
Width = 3 cm
Area = length x width = 5 cm x 3 cm = 15 cm^2
We have two of these faces, so the total area for the top and bottom is:
2 x 15 cm^2 = 30 cm^2
Area of each trapezoidal side:
The top base of each trapezoid is 5 cm (same as the length of the box)
The bottom base is 3 cm (same as the width of the box)
The height is 2 cm
Using the formula for the area of a trapezoid:
Area = [(top base + bottom base) / 2] x height
Area = [(5 cm + 3 cm) / 2] x 2 cm = 8 cm^2
We have four of these faces, so the total area for the sides is:
4 x 8 cm^2 = 32 cm^2
Adding up the areas of all the faces:
30 cm^2 (top and bottom) + 32 cm^2 (sides) = 62 cm^2
Therefore, the surface area of the box is approximately 62 square centimeters.