Question

geometry sem2
final exam assessment
question 2: provide a scenario where math concepts can apply to real world situations.
in a complete paragraph, pick a scenario where concepts from this course would be used - it could be in your own life, it could be in a specific work field such as a construction worker, or working in a business, etc.
choose at least 2 - 3 concepts to include, explain your scenario, how these concepts apply, and provide a worked example for each concept.
use the following format:

• topic sentence: 1 concise sentence describing a scenario where concepts from this course could be used.
• supporting detail: 1 - 2 sentences explaining how 1 concept from the class can be applied to the scenario.
• worked example: show a worked example for the concept described above.
• supporting detail: 1 - 2 sentences explaining how 1 concept from the class can be applied to the scenario.
• worked example: show a worked example for the concept described above.
• conclusion: 1 - 2 sentences describing how applying the concepts in this course to a real - life situation helps in understanding the material in the course.

Explanation:

• Topic Sentence: A landscape architect uses geometry concepts when designing a new park.
• Supporting Detail 1: The architect uses the concept of area to determine the amount of grass seed needed for a rectangular lawn section. The formula for the area of a rectangle is \( A = l \times w \), where \( l \) is length and \( w \) is width.
• Worked Example 1: If the lawn is 20 meters long and 15 meters wide, \( A = 20 \times 15 = 300 \) square meters. So, 300 square meters of grass seed is needed.
• Supporting Detail 2: The architect also uses the Pythagorean theorem (\( a^{2}+b^{2}=c^{2} \)) to ensure a triangular flower bed has right - angled sides for symmetry. If one leg (\( a \)) is 3 meters and the other (\( b \)) is 4 meters, \( c=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5 \) meters, so the hypotenuse should be 5 meters for a right angle.
• Worked Example 2: For a triangular flower bed with legs of length 3 m and 4 m, using \( a = 3 \), \( b = 4 \) in \( a^{2}+b^{2}=c^{2} \), we get \( c=\sqrt{9 + 16}=5 \) m. This helps in verifying the right angle for the flower bed's design.
• Conclusion: Applying geometry concepts like area and the Pythagorean theorem to landscape architecture makes abstract math ideas tangible, as it shows how they solve real - world design and measurement problems, thus deepening understanding of the course material.

Answer:

• Topic Sentence: A landscape architect uses geometry concepts when designing a new park.
• Supporting Detail 1: The architect uses the concept of area to determine the amount of grass seed needed for a rectangular lawn section. The formula for the area of a rectangle is \( A = l \times w \), where \( l \) is length and \( w \) is width.
• Worked Example 1: If the lawn is 20 meters long and 15 meters wide, \( A = 20 \times 15 = 300 \) square meters. So, 300 square meters of grass seed is needed.
• Supporting Detail 2: The architect also uses the Pythagorean theorem (\( a^{2}+b^{2}=c^{2} \)) to ensure a triangular flower bed has right - angled sides for symmetry. If one leg (\( a \)) is 3 meters and the other (\( b \)) is 4 meters, \( c=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5 \) meters, so the hypotenuse should be 5 meters for a right angle.
• Worked Example 2: For a triangular flower bed with legs of length 3 m and 4 m, using \( a = 3 \), \( b = 4 \) in \( a^{2}+b^{2}=c^{2} \), we get \( c=\sqrt{9 + 16}=5 \) m. This helps in verifying the right angle for the flower bed's design.
• Conclusion: Applying geometry concepts like area and the Pythagorean theorem to landscape architecture makes abstract math ideas tangible, as it shows how they solve real - world design and measurement problems, thus deepening understanding of the course material.