Question
Calculate the surface of the square pyramid that has a base length of 12 and a slant height of 18 show your work
Answers
GPT 3.5
To calculate the surface area of a square pyramid, we need to find the area of the base and the area of each of the four triangular faces.
First, we calculate the area of the base which is a square with side length of 12.
Area of the base = side^2 = 12^2 = 144 square units
Next, we calculate the area of each triangular face using the formula:
Area of a triangle = (1/2) * base * height
For a square pyramid, the base of each triangular face is 12 (the side length of the base square) and the height is the slant height, which is 18.
Area of each triangular face = (1/2)*12*18 = 108 square units
Now, since there are 4 triangular faces, we multiply the area of one face by 4 to get the total surface area of the pyramid.
Total surface area = 4 * (Area of one triangular face) + Area of base
Total surface area = 4*108 + 144
Total surface area = 432 + 144
Total 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.
First, we calculate the area of the base which is a square with side length of 12.
Area of the base = side^2 = 12^2 = 144 square units
Next, we calculate the area of each triangular face using the formula:
Area of a triangle = (1/2) * base * height
For a square pyramid, the base of each triangular face is 12 (the side length of the base square) and the height is the slant height, which is 18.
Area of each triangular face = (1/2)*12*18 = 108 square units
Now, since there are 4 triangular faces, we multiply the area of one face by 4 to get the total surface area of the pyramid.
Total surface area = 4 * (Area of one triangular face) + Area of base
Total surface area = 4*108 + 144
Total surface area = 432 + 144
Total 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.