How Do You Find the Lateral and Surface Areas of a Regular Pyramid?

A regular pyramid means that the base of the pyramid is a regular polygon, so all the sides are the same
The lateral area (L) is equal to the perimeter of the base (P) times the slant height (script l) of the pyramid
's' stands for the length of one of the sides of the base
The surface area (S) is equal to the lateral area plus the area of the base
B stands for the area of the base: length (l) times width (w)

1. The lateral area is the area of all of the faces that are not bases
1. A lateral face is a face that is not a base
2. The lateral area is equal to the perimeter of the base times the slant height of the pyramid
3. Our base is a square, so its perimeter is 4•s, where 's' is the length of one of the sides
4. For our pyramid, s=4
5. The slant height of our pyramid is 6
1. Remember, our base here is a square
2. So we need to find the area of that square so we can find the surface area
1. The area of a square is just the length times the width
2. And since it is a square, the length and width are the same, which for our pyramid is 4 cm
3. So the area of the base is just 4•4, or 16 cm²
1. The surface area is just the lateral area plus the area of the base
1. Our lateral area was 48 cm²
2. The area of the base was 16 cm²
3. So the surface area of the pyramid is just 48+16, or 64 cm²

Find the lateral and surface areas of this regular pyramid