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, and then sum them up. Here are the steps:
1. Calculate the area of the base.
The base of the pyramid is a square, so the area of the base (A_base) is given by:
\[ A_{\text{base}} = \text{side length}^2 \]
With the side length being 12, we have:
\[ A_{\text{base}} = 12^2 = 144 \text{ square units} \]
2. Calculate the area of one triangular face.
The area of one triangular face (A_triangle) is given by:
\[ A_{\text{triangle}} = \frac{1}{2} \times \text{base length} \times \text{slant height} \]
The base length of the triangle is the same as the side length of the square, which is 12, and the slant height is given as 18:
\[ A_{\text{triangle}} = \frac{1}{2} \times 12 \times 18 = \frac{1}{2} \times 216 = 108 \text{ square units} \]
3. Calculate the total area of the four triangular faces.
Since there are four triangular faces on the pyramid:
\[ \text{Total area of triangles} = 4 \times A_{\text{triangle}} = 4 \times 108 = 432 \text{ square units} \]
4. Calculate the total surface area of the pyramid.
The total surface area (SA) is the sum of the area of the base and the area of the four triangular faces:
\[ \text{SA} = A_{\text{base}} + \text{Total area of triangles} \]
\[ \text{SA} = 144 + 432 = 576 \text{ square units} \]
Therefore, the surface area of the square pyramid is \( 576 \text{ square units} \).
All steps are shown and clearly explained. The answer is correct and demonstrates proper problem-solving skills and reasoning.
Points awarded: 2
Surface Area Unit Test15 of 15 15 of 15 ItemsQuestionCalculate 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)BoldItalicUnderlineIncrease indentDecrease indentFormula keypadUndoRedo Math Short Answer Rubric (2 points)Points Awarded Criteria2 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.
1 answer
1 answer