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Surface Area of Triangular Prisms Quick Check
2 of 52 of 5 Items
Question
Which of the following describes a valid method for calculating the surface area of a triangular prism?(1 point)
Responses

Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of one triangle and three times the area of one rectangle.
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of one triangle and three times the area of one rectangle.

Decompose the triangular prism into three triangles and two rectangles. Find the sum of three times the area of one triangle and twice the area of one rectangle.
Decompose the triangular prism into three triangles and two rectangles. Find the sum of three times the area of one triangle and twice the area of one rectangle.

Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes.
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes.

Decompose the triangular prism into three triangles and two rectangles. Find the sum of the area of all five shapes.
Decompose the triangular prism into three triangles and two rectangles. Find the sum of the area of all five shapes.
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1 answer

To calculate the surface area of a triangular prism effectively, you need to consider the geometry of the prism. A triangular prism consists of two triangular bases and three rectangular lateral faces.

The correct method for calculating the surface area of a triangular prism is:

Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of both triangles and the areas of the three rectangles.

Since this specific wording isn't in your list, let's analyze the responses you've provided:

  1. Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of one triangle and three times the area of one rectangle. - This is incorrect; it does not account for both triangles.

  2. Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of one triangle and three times the area of one rectangle. - This is also incorrect for the same reason.

  3. Decompose the triangular prism into three triangles and two rectangles. Find the sum of three times the area of one triangle and twice the area of one rectangle. - Incorrect; a triangular prism does not have three triangular faces.

  4. Decompose the triangular prism into three triangles and two rectangles. Find the sum of three times the area of one triangle and twice the area of one rectangle. - Also incorrect for the same reason.

  5. Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes. - This is the correct reasoning because it acknowledges both triangles and the three rectangles in the surface area calculation.

  6. Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes. - Same as above, this is correct.

  7. Decompose the triangular prism into three triangles and two rectangles. Find the sum of the area of all five shapes. - Incorrect; a triangular prism does not have three triangular faces.

  8. Decompose the triangular prism into three triangles and two rectangles. Find the sum of the area of all five shapes. - Incorrect for the same reason as point 7.

Given this analysis, the best response from your list appears to be that which states the correct decomposition into two triangles and three rectangles, and sums the area of all five shapes. This effectively covers the needed computation for surface area. You may choose either response that reflects this method accurately—responses 5 or 6 seem to correctly outline the approach needed.