Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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**Educational Exercise on Geometry** **Figure Overview:** The provided shape is a composite figure consisting of a small square joined with a larger square. There’s a shaded part in the upper right corner of the larger square forming an L-shape when combined. **Steps:** **3.5** Write an expression representing the area of the shaded part. ______________________________________________________ **3.6** Extend a line from the top of the small square (length \( b \)) to the right, going up until it meets the side of the original square. There should now be a rectangle formed adjacent to the smaller square. **3.7** What is the rectangle’s length and breadth, in step 3.6, in terms of \( a \) and \( b \)? - **Length:** ________________________________________ - **Breadth:** _______________________________________ **3.8** Cut out the small square and set it aside. (Use diagram sheet.) **3.9** Cut out the rectangle, lay and stick it alongside the leftover part to form a larger rectangle. Ensure that two sides of the same length are next to each other (the rectangle will need to turn). **3.10** What is the **new** rectangle's length and breadth in terms of \( a \) and \( b \)? - **Length:** ________________________________________ - **Breadth:** _______________________________________ **Diagram Explanation:** The given figure depicts a geometric shape where a small square of side \( b \) is shaded and part of a large square of side \( a \). By following the instructions, you will manipulate this shape to investigate areas and rearrange components to form new figures. Follow the instructions step-by-step to explore these geometric transformations.
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Transcribed Image Text:**Educational Exercise on Geometry** **Figure Overview:** The provided shape is a composite figure consisting of a small square joined with a larger square. There’s a shaded part in the upper right corner of the larger square forming an L-shape when combined. **Steps:** **3.5** Write an expression representing the area of the shaded part. ______________________________________________________ **3.6** Extend a line from the top of the small square (length \( b \)) to the right, going up until it meets the side of the original square. There should now be a rectangle formed adjacent to the smaller square. **3.7** What is the rectangle’s length and breadth, in step 3.6, in terms of \( a \) and \( b \)? - **Length:** ________________________________________ - **Breadth:** _______________________________________ **3.8** Cut out the small square and set it aside. (Use diagram sheet.) **3.9** Cut out the rectangle, lay and stick it alongside the leftover part to form a larger rectangle. Ensure that two sides of the same length are next to each other (the rectangle will need to turn). **3.10** What is the **new** rectangle's length and breadth in terms of \( a \) and \( b \)? - **Length:** ________________________________________ - **Breadth:** _______________________________________ **Diagram Explanation:** The given figure depicts a geometric shape where a small square of side \( b \) is shaded and part of a large square of side \( a \). By following the instructions, you will manipulate this shape to investigate areas and rearrange components to form new figures. Follow the instructions step-by-step to explore these geometric transformations.
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