To calculate the surface area of a pyramid S, we can use the known formula where P is the perimeter of the base, l is the slant height, and B is the area of the base.
S=1/2Pl+BThe base of the pyramid is a square with the side length s of 4in. Now let's find the perimeter of the base, which is equal to four times the side length s.
P=4(s) ⇒ P&=4( 4) P&= 16in
The area of the square is equal to the square of the side length s.
B=s^2 ⇒ B&= 4^2 B&= 16in^2
To find the slant height, we can use the Pythagorean Theorem. When doing this, the slant height l is the hypotenuse. The height and apothem, which is half the side length of the pyramid, are the legs. By substituting height h with 9 and apothem a with 4÷ 2= 2, we can solve for l.
When solving the above equation, we only kept the principal root because l must be positive. Now, we can substitute l with sqrt(85), P with 16 and B with 16 in the formula for the surface area.
