Answer:
surface area = 1536 cm^2
Explanation:
The surface area of a square pyramid can be found using the formula:
surface area = base area + 1/2 * perimeter * slant height
The base area is the area of a square, which is given by base length squared:
base area = (24 cm)^2 = 576 cm^2
The perimeter of the base is the sum of the lengths of its sides, which is 4 times the base length:
perimeter = 4 * 24 cm = 96 cm
The slant height can be found using the Pythagorean theorem:
slant height^2 = height^2 + (base length/2)^2
slant height^2 = (16 cm)^2 + (12 cm)^2
slant height = sqrt[(16 cm)^2 + (12 cm)^2] ≈ 20 cm
Therefore, the surface area of the square pyramid is:
surface area = base area + 1/2 * perimeter * slant height
surface area = 576 cm^2 + 1/2 * 96 cm * 20 cm
surface area = 576 cm^2 + 960 cm^2
surface area = 1536 cm^2