The first thing we should know is that since it's a rectangular prism, there could be 3 different pairs of bases here. To start, we'll stay that the 7 cm × 2 cm side is our base. *SA* = *L* + 2*B*
*SA* = *Ph* + 2*B*
The perimeter of our base is 7 + 2 + 7 + 2, or 18 cm. The height is 13 cm. Our rectangular bases are equal to their length times their width, or 7 cm × 2 cm = 14 cm^{2}. *SA* = (18 cm)(13 cm) + 2(14 cm^{2})
*SA* = 234 cm^{2} + 28 cm^{2} = 262 cm^{2}
That means the surface area is 262 cm^{2}, and the lateral area when the base is 7 cm × 2 cm is 234 cm^{2}. If the bases were the 7 cm × 13 cm sides, our lateral surface area would be different. The perimeter would be 7 + 13 + 7 + 13 = 40 cm, and our height would be 2 cm. Since *L* = *Ph*, our lateral area would be (40 cm)(2 cm) = 80 cm^{2}. One last base pair: the 2 cm × 13 cm sides. The perimeter would be 30 cm and the height is 7 cm, so the lateral area is *L* = *Ph* = (30 cm)(7 cm) = 210 cm^{2}. Notice that while the lateral area changes depending on the bases we use, the surface area for the prism stays the same. That makes sense, because we don't use a different amount of wrapping paper just because the object is facing a different way. Unless you do, which would be weird. |