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
To calculate the surface area of a 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:
Area of square base = (side length)^2
Area of square base = 12^2
Area of square base = 144
Next, let's find the area of one of the triangular faces:
Area of triangular face = (1/2) * base * height
Area of triangular face = (1/2) * 12 * 18
Area of triangular face = 108
Since there are 4 triangular faces on a square pyramid, the total area of the triangular faces is:
Total area of triangular faces = 4 * 108
Total area of triangular faces = 432
Now, we can calculate the total surface area of the square pyramid by adding the area of the base and the total area of the triangular faces:
Surface area = Area of base + Total area of triangular faces
Surface area = 144 + 432
Surface area = 576
Therefore, the surface area of the square pyramid is 576.
shorter
Sure! We can represent the surface area of a square pyramid with base length \(b\) and slant height \(s\) as:
\[A = b^2 + 2bs\]
Given that the base length is 12 and the slant height is 18, we can substitute these values into the formula:
\[A = 12^2 + 2(12)(18)\]
\[A = 144 + 432\]
\[A = 576\]
Therefore, the surface area of the square pyramid is 576 square units.
keep that but just change therefore to so
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Sure! Here is the revised explanation:
Given that the base length is 12 and the slant height is 18, we can calculate the surface area using the formula \(A = b^2 + 2bs\).
So, substituting the values:
\[A = 12^2 + 2(12)(18)\]
\[A = 144 + 432\]
\[A = 576\]
The surface area of the square pyramid is 576 square units.