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14. 6. 3 18 6.

14. 6. 3 18 6.

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 area and perimeter of each of the following:

**Transcription and Explanation for Educational Website** --- **Geometry Problems: Analysis and Practice** **Problem 14** In this diagram, we are presented with a composite geometric shape composed of rectangles and L-shapes. The dimensions are given by the following measurements (all measurements are in the same unit): - The topmost horizontal segment is 5 units. - The vertical segment connected to it on the left is 6 units. - Moving horizontally to the right from there, the segment is 3 units. - A vertical drop of 5 units follows next. - Moving left again, the horizontal segment is 5 units, aligning parallel to the previous segment. - A vertical segment of 6 units descends, connecting to the bottommost 7-unit horizontal base. - The internal height of the L-shape on the right side is 18 units from top to bottom. This layout can be visualized as a collection of simpler shapes like rectangles that can help in calculating areas, perimeters, etc. **Problem 15** This diagram shows another composite shape with dimensions well-defined, consisting primarily of rectangles coupled with a central cut-out. The dimensions are: - The topmost left vertical segment is 8 units. - Descending right, the next vertical segments on both sides of the cut-out are 10 units each. - Between these two vertical segments, there's a horizontal cut-out segment measuring 6 units. - The bottommost horizontal segment spans 22 units in total. This shape is useful in visualizing geometric problem-solving strategies such as calculating the area of composite shapes by breaking them into smaller, manageable parts. --- **Graph/Diagram Description** Both shapes in Problem 14 and Problem 15 are designed to test the ability to deduce area and perimeter by working with composite figures. The first shape (Problem 14) involves a step-like structure, while the second shape (Problem 15) demonstrates a block with a rectangular cut-out from the top center. Important Geometry Concepts Covered: - Composite shapes - Calculating areas and perimeters - Visualizing geometric transformations These exercises are fundamental in understanding complex geometric configurations through simpler components.
Transcribed Image Text:**Transcription and Explanation for Educational Website** --- **Geometry Problems: Analysis and Practice** **Problem 14** In this diagram, we are presented with a composite geometric shape composed of rectangles and L-shapes. The dimensions are given by the following measurements (all measurements are in the same unit): - The topmost horizontal segment is 5 units. - The vertical segment connected to it on the left is 6 units. - Moving horizontally to the right from there, the segment is 3 units. - A vertical drop of 5 units follows next. - Moving left again, the horizontal segment is 5 units, aligning parallel to the previous segment. - A vertical segment of 6 units descends, connecting to the bottommost 7-unit horizontal base. - The internal height of the L-shape on the right side is 18 units from top to bottom. This layout can be visualized as a collection of simpler shapes like rectangles that can help in calculating areas, perimeters, etc. **Problem 15** This diagram shows another composite shape with dimensions well-defined, consisting primarily of rectangles coupled with a central cut-out. The dimensions are: - The topmost left vertical segment is 8 units. - Descending right, the next vertical segments on both sides of the cut-out are 10 units each. - Between these two vertical segments, there's a horizontal cut-out segment measuring 6 units. - The bottommost horizontal segment spans 22 units in total. This shape is useful in visualizing geometric problem-solving strategies such as calculating the area of composite shapes by breaking them into smaller, manageable parts. --- **Graph/Diagram Description** Both shapes in Problem 14 and Problem 15 are designed to test the ability to deduce area and perimeter by working with composite figures. The first shape (Problem 14) involves a step-like structure, while the second shape (Problem 15) demonstrates a block with a rectangular cut-out from the top center. Important Geometry Concepts Covered: - Composite shapes - Calculating areas and perimeters - Visualizing geometric transformations These exercises are fundamental in understanding complex geometric configurations through simpler components.
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