The base of a pyramid is a square. The perimeter of the base is 20ft, and the surface area of the pyramid is 65ft^2. Find the slant height of the pyramid.

base is a 5 by 5 square

is the base included in the surface area ?

can I use tha formula is SA = b + 1/2pl?

8ougyogy

To find the slant height of the pyramid, we can use the Pythagorean theorem by creating a right triangle with the slant height as the hypotenuse.

First, let's find the length of one side of the square base. Since the perimeter of the base is 20ft and the base is a square, each side length of the square will be equal.

The formula for the perimeter of a square is P = 4s, where P is the perimeter and s is the side length. In this case, the perimeter is 20ft, so we can set up the equation:

20 = 4s

Dividing both sides of the equation by 4:

s = 5ft

Now, let's find the area of one face of the pyramid. Since the surface area of the entire pyramid is 65ft^2 and the base is a square, each face of the pyramid will be identical.

The formula for the surface area of a pyramid is A = 1/2 * P * l, where A is the surface area, P is the perimeter of the base, and l is the slant height. In this case, we can use the area formula to solve for the slant height:

65 = 1/2 * 20 * l

Multiplying both sides of the equation by 2:

130 = 20 * l

Dividing both sides of the equation by 20:

l = 6.5ft

Therefore, the slant height of the pyramid is 6.5ft.