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.
1. First, calculate the area of the base:
Given that the base length is 12, the area of the square base is:
Area_base = (base length)^2
Area_base = 12^2
Area_base = 144 square units
2. Next, calculate the area of the four triangular faces:
The slant height of the pyramid is given as 18, and each face is a triangle with base length equal to the base length of the square base (12) and height equal to the slant height (18).
The area of each triangular face can be calculated using the formula for the area of a triangle: Area_triangle = 0.5 x base x height
Area_triangle = 0.5 x 12 x 18
Area_triangle = 108 square units
Since there are 4 identical triangular faces, the total surface area of the four triangular faces is:
Total_area_triangular_faces = 4 x 108
Total_area_triangular_faces = 432 square units
3. Finally, calculate the total surface area of the square pyramid:
Total_surface_area = Area_base + Total_area_triangular_faces
Total_surface_area = 144 + 432
Total_surface_area = 576 square units
Therefore, the surface area of the square pyramid 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)
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shorter response
The surface area of the square pyramid with a base length of 12 and a slant height of 18 is 576 square units.
To calculate the surface area, find the area of the base (12^2 = 144 square units) and the area of the four triangular faces (4 x 0.5 x 12 x 18 = 432 square units), then add them together (144 + 432 = 576 square units).
To calculate the surface area, find the area of the base (12^2 = 144 square units) and the area of the four triangular faces (4 x 0.5 x 12 x 18 = 432 square units), then add them together (144 + 432 = 576 square units).
What does the ^ mean?
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