Final answer:
To calculate the surface area of a square pyramid, find the area of the base and the areas of the four triangular faces. Use the formula A = 1/2 * base * slant height to find the area of each triangular face. Then, add the areas together to get the total surface area.
Step-by-step explanation:
A square pyramid has a base in the shape of a square and four triangular faces that meet at a common vertex called the apex. To calculate the surface area of a square pyramid, you need to find the area of the square base and the areas of the four triangular faces.
The formula for the area of a triangle is A = 1/2 * base * height. Since the height of a triangular face of the pyramid is equal to its slant height, we can find the area of each triangular face using the formula A = 1/2 * base * slant height. Finally, we add the areas of the base and the four triangular faces to get the total surface area of the square pyramid.
In this case, the base of the pyramid has an edge length of 2 centimeters and the height of the pyramid is 9 centimeters. We can now use the formulas mentioned above to calculate the surface area of the pyramid.
Surface area of pyramid = Area of base + 4 * Area of triangular faces
Area of square base = (edge length)^2 = 2^2 = 4 square centimeters
Area of triangular face = (1/2 * base * slant height) = (1/2 * 2 * slant height) = slant height
Since the slant height of each triangular face is equal to the height of the pyramid, which is 9 centimeters, we can substitute the slant height with 9 in the formula:
Area of triangular face = 9 square centimeters
Now, we can calculate the surface area of the pyramid:
Surface area of pyramid = 4 + (4 * 9) = 4 + 36 = 40 square centimeters