To calculate the surface area of a square pyramid, you can use the formula:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
First, we need to calculate the base area of the square pyramid:
Base Area = s^2 (where s is the length of the base)
Base Area = 12^2 = 144 square units
Next, we need to calculate the perimeter of the base (P) by multiplying the length of one side by 4 since a square has equal sides:
P = 4s
P = 4 * 12
P = 48
Now, we can calculate the surface area of the square pyramid:
Surface Area = 144 + (1/2) * 48 * 18
Surface Area = 144 + 432
Surface Area = 576 square units
Therefore, the surface area of the square pyramid with a base length of 12 and a slant height of 18 is 576 square units.
Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18. Show your work.(2 points
make it understandable and show me the formula
3 answers
why are we dividing by 2
We are dividing by 2 in the formula for the surface area of a pyramid because the slant height connects the base to the apex of the pyramid, creating two triangular faces for each side of the base. Dividing by 2 ensures that we are calculating the total area of both triangular faces rather than just one.
The formula for the surface area of a pyramid includes the factor of 1/2 to account for this and provide an accurate measurement of the total surface area of the pyramid.
Therefore, the 1/2 in the formula represents the fact that we are finding the sum of two triangular faces for each side of the base when calculating the surface area of the pyramid.
The formula for the surface area of a pyramid includes the factor of 1/2 to account for this and provide an accurate measurement of the total surface area of the pyramid.
Therefore, the 1/2 in the formula represents the fact that we are finding the sum of two triangular faces for each side of the base when calculating the surface area of the pyramid.
1 answer