Find the lateral area and the surface area of the solid.
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 + 2B SA = Ph + 2B
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 cm2.
SA = (18 cm)(13 cm) + 2(14 cm2) SA = 234 cm2 + 28 cm2 = 262 cm2
That means the surface area is 262 cm2, and the lateral area when the base is 7 cm × 2 cm is 234 cm2.
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 cm2.
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 cm2.
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.