Answer:
To calculate the surface area of a square pyramid, we need to find the area of the base and the area of each triangular face, then add them together.
First, let's find the area of the base:
Area of square base = (side length)^2 = (15m)^2 = 225m²
Next, let's find the area of each triangular face:
Area of triangular face = (1/2) x (base length) x (height)
The base length of each triangular face is equal to the side length of the square base, which is 15m. We need to find the height of the pyramid to calculate the area of each triangular face.
To do this, we can use the Pythagorean theorem. Since the pyramid is a right pyramid (meaning the apex is directly above the center of the square base), the height is the hypotenuse of a right triangle with legs equal to half the length of one side of the base. Thus, the height can be found as follows:
height = sqrt((side length/2)^2 + height^2)
We can simplify this to:
height^2 = side length^2 - (side length/2)^2
height^2 = 225 - 56.25
height^2 = 168.75
height = sqrt(168.75)
height ≈ 12.99m
Now we can calculate the area of each triangular face:
Area of triangular face = (1/2) x (base length) x (height)
Area of triangular face = (1/2) x 15m x 12.99m
Area of triangular face ≈ 97.43m²
Finally, we can add the area of the base and the area of the four triangular faces together to get the total surface area:
Total surface area = area of base + 4 x area of triangular face
Total surface area = 225m² + 4 x 97.43m²
Total surface area ≈ 620.72m²
Therefore, the answer is A. 620.72 m².
Explanation: