How Do You Find the Lateral and Surface Areas of a Rectangular Prism?

The lateral area is the sum of the areas of all the lateral faces
Lateral faces are the faces of the prism that aren't bases
Lateral area, L, is equal to the perimeter of the base, P, times the height of the prism, h
B is the area of one of the rectangular bases
S is the surface area

1. The lateral area is the area of all the lateral faces added together
2. Lateral faces are the faces of the prism that aren't bases
1. Lateral faces are the faces of the prism that aren't bases
1. The perimeter of the base is 2l+2w, where 'l' and 'w' are the length and width of the rectangle
2. So the lateral area is (2l+2w)•h, where h is the height of the prism
3. Here l=12, w=6, and h=7
4. So the lateral area is (2(12)+2(6))•7, which simplifies to 252 m²
1. In this case, the base is a rectangle
1. Then we can just multiply the area of one base by 2 to get the area of both bases
1. Remember, the length of our rectangle is 12 m and the width is 6 m
2. So the area of one base is 12•6, or 72 m²
1. Remember, the surface area is just the lateral area plus the area of the bases
1. We found the lateral area to be 252m² and the area of ONE of the bases to be 72m²
2. But we have TWO bases, so we need to multiply 72 by 2
3. 252+72•2=396

Find the lateral and surface areas of the rectangular prism.