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The net shown below represents a triangular prism. 18 in 6 in 8 in Which statements are true? Choose all that are correct. A. The surface area of the prism is 264 square inches. В. The surface area of the prism is 372 square inches. The total area of the two triangular bases of the prism is 48 square inches. D. The total area of the rectangular faces of the prism is 324 square inches. Е. The surface area of the prism is 312 square inches. F. The total area of the two triangular bases of the prism is 96 square inches. C.

The net shown below represents a triangular prism. 18 in 6 in 8 in Which statements are true? Choose all that are correct. A. The surface area of the prism is 264 square inches. В. The surface area of the prism is 372 square inches. The total area of the two triangular bases of the prism is 48 square inches. D. The total area of the rectangular faces of the prism is 324 square inches. Е. The surface area of the prism is 312 square inches. F. The total area of the two triangular bases of the prism is 96 square inches. C.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Understanding the Net of a Triangular Prism The diagram shown below is a net representation of a triangular prism. When folded, this net forms the three-dimensional shape of the prism. #### Diagram Explanation: - The net includes the following dimensions: - **Length of the Rectangle:** 18 inches - **Width of the Rectangle:** 6 inches - **Base of the Triangle:** 8 inches - **Height of the Triangle:** 6 inches #### Quiz: Which Statements Are True? Choose all that are correct. A. ☐ The surface area of the prism is 264 square inches. B. ☐ The surface area of the prism is 372 square inches. C. ☐ The total area of the two triangular bases of the prism is 48 square inches. D. ☐ The total area of the rectangular faces of the prism is 324 square inches. E. ☐ The surface area of the prism is 312 square inches. F. ☐ The total area of the two triangular bases of the prism is 96 square inches. ### How to Calculate the Surface Area of a Triangular Prism 1. **Calculate the area of one triangular base:** - Area of a triangle = 1/2 * base * height - Area = 1/2 * 8 in * 6 in = 24 square inches 2. **Calculate the total area of the two triangular bases:** - Total area = 2 * 24 square inches = 48 square inches 3. **Calculate the area of the three rectangular faces:** - The rectangular faces dimensions are 6 in x 18 in (two of these) and 8 in x 18 in (one of these). - Area of the two rectangular faces = 2 * (6 in * 18 in) = 2 * 108 square inches = 216 square inches - Area of the remaining rectangular face = 8 in * 18 in = 144 square inches - Total area of the rectangular faces = 216 square inches + 144 square inches = 360 square inches 4. **Calculate the total surface area:** - Total surface area = area of triangular bases + area of rectangular faces - Total surface area = 48 square inches + 360 square inches = 408 square inches Use the above steps to verify which of the statements (A
Transcribed Image Text:### Understanding the Net of a Triangular Prism The diagram shown below is a net representation of a triangular prism. When folded, this net forms the three-dimensional shape of the prism. #### Diagram Explanation: - The net includes the following dimensions: - **Length of the Rectangle:** 18 inches - **Width of the Rectangle:** 6 inches - **Base of the Triangle:** 8 inches - **Height of the Triangle:** 6 inches #### Quiz: Which Statements Are True? Choose all that are correct. A. ☐ The surface area of the prism is 264 square inches. B. ☐ The surface area of the prism is 372 square inches. C. ☐ The total area of the two triangular bases of the prism is 48 square inches. D. ☐ The total area of the rectangular faces of the prism is 324 square inches. E. ☐ The surface area of the prism is 312 square inches. F. ☐ The total area of the two triangular bases of the prism is 96 square inches. ### How to Calculate the Surface Area of a Triangular Prism 1. **Calculate the area of one triangular base:** - Area of a triangle = 1/2 * base * height - Area = 1/2 * 8 in * 6 in = 24 square inches 2. **Calculate the total area of the two triangular bases:** - Total area = 2 * 24 square inches = 48 square inches 3. **Calculate the area of the three rectangular faces:** - The rectangular faces dimensions are 6 in x 18 in (two of these) and 8 in x 18 in (one of these). - Area of the two rectangular faces = 2 * (6 in * 18 in) = 2 * 108 square inches = 216 square inches - Area of the remaining rectangular face = 8 in * 18 in = 144 square inches - Total area of the rectangular faces = 216 square inches + 144 square inches = 360 square inches 4. **Calculate the total surface area:** - Total surface area = area of triangular bases + area of rectangular faces - Total surface area = 48 square inches + 360 square inches = 408 square inches Use the above steps to verify which of the statements (A
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