first one:
The surface area of a pyramid can be found using the formula:
Surface Area = (1/2) x Perimeter of Base x Slant Height + Base Area
Since the side lengths of the base are equal, the perimeter of the base is:
Perimeter of Base = 4 x Side Length
Perimeter of Base = 4 x 9 = 36 feet
To find the slant height, we can use the Pythagorean theorem:
Slant Height^2 = Height^2 + (1/2 x Side Length)^2
Slant Height^2 = 12^2 + (1/2 x 9)^2
Slant Height^2 = 144 + 20.25
Slant Height^2 = 164.25
Slant Height = 12.81 feet
The base area can be found using the formula for the area of a square:
Base Area = Side Length^2
Base Area = 9^2 = 81 square feet
Plugging in the values into the formula for surface area:
Surface Area = (1/2) x 36 x 12.81 + 81
Surface Area = 218.16 square feet
So the surface area of the pyramid is 218.16 square feet.
second one:
The surface area of a pyramid can be found using the formula:
Surface Area = (1/2) x Perimeter of Base x Slant Height + Base Area
Since the side lengths of the base are equal, the perimeter of the base is:
Perimeter of Base = 4 x Side Length
Perimeter of Base = 4 x 8 = 32 meters
To find the slant height, we can use the Pythagorean theorem:
Slant Height^2 = Height^2 + (1/2 x (Side Length1 + Side Length2))^2
Slant Height^2 = 3.5^2 + (1/2 x (8 + 4))^2
Slant Height^2 = 12.25 + 36
Slant Height^2 = 48.25
Slant Height = 6.94 meters
The base area can be found using the formula for the area of a square:
Base Area = Side Length^2
Base Area = 8^2 = 64 square meters
Plugging in the values into the formula for surface area:
Surface Area = (1/2) x 32 x 6.94 + 64
Surface Area = 107.52 square meters
So the surface area of the pyramid is 107.52 square meters.