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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)
Math Short Answer Rubric (2 points)
Points Awarded Criteria
2
The answer is correct. The student made no errors while solving.
The answer shows that the student used problem-solving skills and reasoning.
All work is shown or explained.
1
The answer is partially correct. The student made errors while solving.
The answer shows little problem-solving skills or reasoning.
Some work is shown or explained.
0 The question is not answered.
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.
Given:
Base length = 12
Slant height = 18
To find the area of the base:
Area of a square = side length^2
Area of base = 12^2 = 144
To find the area of one triangular face:
Area of a triangle = 0.5 * base * height
Height of the triangular face is the slant height of the pyramid = 18
Area of one triangular face = 0.5 * 12 * 18 = 108
Since the pyramid has four triangular faces, the total area of the four triangular faces is:
Total area of four triangular faces = 4 * 108 = 432
The total surface area of the square pyramid is the sum of the area of the base and the area of the four triangular faces:
Surface area = 144 + 432 = 576
Therefore, the surface area of the square pyramid is 576.