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Find the lateral area and and Surface Area for the following prisms:

Find the lateral area and and Surface Area for the following prisms:

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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Find the lateral area and and Surface Area for the following prisms:

**Trapezoidal Prism Dimensions** The following diagram illustrates a trapezoidal prism. The dimensions are labeled and specific lengths are provided. Below is a detailed description of each part of the shape: 1. **Top Face**: This is a trapezoid with the following dimensions: - Top side length = 5 units - Two slanted sides, each of a length of √5 units (indicating these sides are equivalent diagonals). 2. **Bottom Face**: This also constitutes a trapezoid with the following dimensions: - Bottom side length = 7 units - Two slanted sides meet to form a small horizontal segment of length 2 units. 3. **Height of the Prism**: The vertical height (distance between the top and bottom trapezoids) is 9 units. By breaking down these dimensions, it becomes clear how this shape can be constructed and understood in a three-dimensional space. This prism's trapezoidal faces and connecting rectangular sides create a solid 3D figure.
Transcribed Image Text:**Trapezoidal Prism Dimensions** The following diagram illustrates a trapezoidal prism. The dimensions are labeled and specific lengths are provided. Below is a detailed description of each part of the shape: 1. **Top Face**: This is a trapezoid with the following dimensions: - Top side length = 5 units - Two slanted sides, each of a length of √5 units (indicating these sides are equivalent diagonals). 2. **Bottom Face**: This also constitutes a trapezoid with the following dimensions: - Bottom side length = 7 units - Two slanted sides meet to form a small horizontal segment of length 2 units. 3. **Height of the Prism**: The vertical height (distance between the top and bottom trapezoids) is 9 units. By breaking down these dimensions, it becomes clear how this shape can be constructed and understood in a three-dimensional space. This prism's trapezoidal faces and connecting rectangular sides create a solid 3D figure.
**Transcription for Educational Website:** **Title:** Understanding Pyramid Dimensions with Triangular Bases **Content:** The diagram depicts a pyramid with a triangular base. Below the image, you will find explanations and descriptions of the key measurements and features of the pyramid. **Diagram Explanation:** 1. **Base Triangle Measurements:** - The base of the triangular face is 6 units. - The perpendicular height of the triangle from the base to the apex inside the pyramid is 4 units. 2. **Lateral Edges:** - The slant height (the length from the apex of the triangular base to the top vertex of the pyramid) on the left side is 5 units. - The slant height on the right side of the triangular face is also 5 units. 3. **Pyramid Dimensions:** - The length of the base along the ground of the pyramid is 12 units. - The height of the pyramid from the base to the top vertex, along the edge, is denoted by the letter "h" (an unknown variable which one needs to calculate based on given dimensions). Additionally, the dashed lines in the diagram represent the internal dimensions used to calculate heights and distances within the triangular cross-sections. This pyramid geometric figure is typically used to understand 3-dimensional geometry concepts, including volume and surface area calculations. **Important Note:** When studying this pyramid, remember to apply the Pythagorean theorem and properties of triangles to solve for unknown dimensions. The given dimensions can help calculate the slant height, lateral surface area, volume, and more. **End of Transcription**
Transcribed Image Text:**Transcription for Educational Website:** **Title:** Understanding Pyramid Dimensions with Triangular Bases **Content:** The diagram depicts a pyramid with a triangular base. Below the image, you will find explanations and descriptions of the key measurements and features of the pyramid. **Diagram Explanation:** 1. **Base Triangle Measurements:** - The base of the triangular face is 6 units. - The perpendicular height of the triangle from the base to the apex inside the pyramid is 4 units. 2. **Lateral Edges:** - The slant height (the length from the apex of the triangular base to the top vertex of the pyramid) on the left side is 5 units. - The slant height on the right side of the triangular face is also 5 units. 3. **Pyramid Dimensions:** - The length of the base along the ground of the pyramid is 12 units. - The height of the pyramid from the base to the top vertex, along the edge, is denoted by the letter "h" (an unknown variable which one needs to calculate based on given dimensions). Additionally, the dashed lines in the diagram represent the internal dimensions used to calculate heights and distances within the triangular cross-sections. This pyramid geometric figure is typically used to understand 3-dimensional geometry concepts, including volume and surface area calculations. **Important Note:** When studying this pyramid, remember to apply the Pythagorean theorem and properties of triangles to solve for unknown dimensions. The given dimensions can help calculate the slant height, lateral surface area, volume, and more. **End of Transcription**
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