A jewelry store buys small boxes in which to wrap items that they sell. The diagram below shows one of the boxes. Find the lateral area and the surface area of the box to the nearest whole number. Use the large 14 x 7 cm rectangles on the top and bottom as the bases.
1.) 35 cm ^2; 364 cm^2
2.) 70 cm^2;364 cm^2
3.) 35 cm^2; 266 cm^2
4.) 70 cm^2; 266 cm^2
The box has six faces. Four of them are rectangles, and two of them are squares.
The lateral area is the sum of the areas of the four rectangles. Each rectangle has a length of 7 cm and a height of 4 cm, so the total lateral area is:
4(7 cm x 4 cm) = 112 cm^2
The surface area includes the two squares on the top and bottom in addition to the four rectangles. Each square has an area of:
14 cm x 14 cm = 196 cm^2
So the total surface area is:
2(196 cm^2) + 112 cm^2 = 504 cm^2
Rounded to the nearest whole number, the lateral area is 112 cm^2 and the surface area is 504 cm^2. Therefore, the answer is option 2.) 70 cm^2;364 cm^2.