To find the surface area of the square pyramid, we need to find the area of the base and the area of the four triangular faces.
First, let's find the area of the base of the square pyramid:
Base length = 12
Base area = length x width = 12 x 12 = 144
Next, let's find the area of one triangular face:
Slant height = 18
Base length = 12
Using the Pythagorean theorem: height = sqrt(18^2 - 12^2) = sqrt(324 - 144) = sqrt(180) = 6√5
Now, let's find the area of one triangular face:
Area = 0.5 x base x height = 0.5 x 12 x 6√5 = 36√5
Since there are 4 triangular faces, the total area of the triangular faces is:
4 x 36√5 = 144√5
Finally, to find the surface area we add the area of the base and the area of the triangular faces:
Surface area = base area + triangular faces area = 144 + 144√5 = 144 + 144 x 2.236 = 144 + 321.384 = 465.384
So, the surface area of the square pyramid is 465.384 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
write as a 7th grader
5 answers
make it shorter
To find the surface area of a pyramid with a base length of 12 and a slant height of 18, we calculate the area of the base (12 x 12 = 144) and the four triangular faces (4 x 0.5 x base x height = 4 x 0.5 x 12 x 6√5 = 144√5).
The total surface area is the sum of the base area and the triangular faces area (144 + 144√5 = 465.384).
Therefore, the surface area of the square pyramid is 465.384 square units.
The total surface area is the sum of the base area and the triangular faces area (144 + 144√5 = 465.384).
Therefore, the surface area of the square pyramid is 465.384 square units.
write as a 7th grader
To find the surface area of a pyramid with a base length of 12 and a slant height of 18, we first calculate the area of the base by multiplying 12 by 12 to get 144 square units. Then, we find the area of the four triangular faces by using the formula for the area of a triangle (0.5 x base x height) and multiplying by 4, resulting in 144√5 square units.
By adding the base area and the area of the triangular faces (144 + 144√5 = 465.384), we get the total surface area of the square pyramid as 465.384 square units.
By adding the base area and the area of the triangular faces (144 + 144√5 = 465.384), we get the total surface area of the square pyramid as 465.384 square units.