What is the surface area of the square pyramid?
Responses
1,296 m²
1,296 m² , EndFragment,
2,160 m²
3,456 m²
9,984 m²
To calculate the surface area of a square pyramid, you can use the formula:
Surface Area = Base Area + 4 x (1/2 x Perimeter of Base x Slant Height)
Given that the base of the square pyramid is a square, the perimeter of the base is 4 x side length of the base (squared). Let's assume the side length of the base is x, and the slant height is also x.
Base Area = x^2
Perimeter of Base = 4x
Slant Height = x
Now, plug these values into the formula:
Surface Area = x^2 + 4 x (1/2 x 4x x)
Surface Area = x^2 + 4 x (2x^2)
Surface Area = x^2 + 8x^2
Surface Area = 9x^2
If the area of the square pyramid is 1,296 m², then:
9x^2 = 1,296
x^2 = 144
x = 12
Therefore, the side length of the base of the square pyramid is 12 m.
Now, calculate the surface area using the side length:
Surface Area = 9 x (12^2)
Surface Area = 9 x 144
Surface Area = 1,296 m²
Therefore, the surface area of the square pyramid is 1,296 m².