Lesson 2 Exam: Polygons And Triangles Exam Number: 700193RR Question 5 Of 20: Select The Best Answer For The Question.On An Architect's Plan For A House, The Scale Reads 1/2 In. = 5 Ft. How Many Feet Does 3 Inches Represent On The Plan?A. 10 Ft. B.
Lesson 2 Exam: Polygons and Triangles Exam Number: 700193RR Question 5 of 20:
When working with architectural plans, it's essential to understand the scale and measurement to accurately represent the design. In this question, we're given a scale of 1/2 in. = 5 ft. and asked to find the equivalent measurement in feet for 3 inches on the plan.
The Scale and Its Significance
The given scale, 1/2 in. = 5 ft., indicates that every half inch on the plan represents 5 feet in real life. This means that the plan is scaled down to make it easier to work with, and we need to use this scale to convert measurements between the plan and the actual building.
Converting Inches to Feet
To find the equivalent measurement in feet for 3 inches on the plan, we need to use the scale to convert inches to feet. Since 1/2 inch represents 5 feet, we can set up a proportion to find the equivalent measurement for 3 inches.
Setting Up the Proportion
Let's set up a proportion to find the equivalent measurement in feet for 3 inches:
1/2 in. = 5 ft. 3 in. = x ft.
We can write this as a proportion:
(1/2 in.) / (5 ft.) = (3 in.) / x ft.
Solving the Proportion
To solve the proportion, we can cross-multiply:
1/2x = 3(5)
Simplifying the equation, we get:
1/2x = 15
Multiplying both sides by 2 to isolate x, we get:
x = 30
The Final Answer
Therefore, 3 inches on the plan represents 30 feet in real life.
Conclusion
In this question, we used the given scale to convert inches to feet. By setting up a proportion and solving for x, we found that 3 inches on the plan represents 30 feet in real life. This demonstrates the importance of understanding scale and measurement in architecture, as it allows us to accurately represent the design and make informed decisions about the building's construction.
Key Takeaways
- The scale 1/2 in. = 5 ft. indicates that every half inch on the plan represents 5 feet in real life.
- To convert inches to feet, we can set up a proportion using the scale.
- Solving the proportion allows us to find the equivalent measurement in feet for a given number of inches on the plan.
Practice Problems
- If the scale is 1/4 in. = 10 ft., how many feet does 6 inches represent on the plan?
- If the scale is 1/8 in. = 20 ft., how many feet does 4 inches represent on the plan?
Answer Key
- 60 ft.
- 40 ft.
Additional Resources
For more practice problems and resources on scale and measurement in architecture, check out the following links:
Final Thoughts
Understanding scale and measurement is crucial in architecture, as it allows us to accurately represent the design and make informed decisions about the building's construction. By practicing with proportions and converting inches to feet, we can become more confident in our ability to work with architectural plans.
Lesson 2 Exam: Polygons and Triangles
Exam Number: 700193RR
Question 5 of 20:
Q: What is a polygon?
A: A polygon is a two-dimensional shape with at least three straight sides and three vertices (corners). Polygons can be classified into different types, such as triangles, quadrilaterals, pentagons, and so on.
Q: What is a triangle?
A: A triangle is a polygon with three straight sides and three vertices. Triangles can be classified into different types, such as acute, right, and obtuse triangles, based on the measure of their angles.
Q: What is the difference between an acute triangle and a right triangle?
A: An acute triangle is a triangle with all angles measuring less than 90 degrees. A right triangle is a triangle with one angle measuring exactly 90 degrees.
Q: What is the difference between a right triangle and an obtuse triangle?
A: A right triangle is a triangle with one angle measuring exactly 90 degrees. An obtuse triangle is a triangle with one angle measuring greater than 90 degrees.
Q: What is the sum of the interior angles of a triangle?
A: The sum of the interior angles of a triangle is always 180 degrees.
Q: What is the formula for finding the area of a triangle?
A: The formula for finding the area of a triangle is:
Area = (base × height) / 2
Q: What is the formula for finding the perimeter of a triangle?
A: The formula for finding the perimeter of a triangle is:
Perimeter = a + b + c
where a, b, and c are the lengths of the sides of the triangle.
Q: What is the difference between a regular polygon and an irregular polygon?
A: A regular polygon is a polygon with all sides and angles equal. An irregular polygon is a polygon with sides and angles of different lengths and measures.
Q: What is the formula for finding the area of a regular polygon?
A: The formula for finding the area of a regular polygon is:
Area = (n × s^2) / (4 × tan(π/n))
where n is the number of sides and s is the length of one side.
Q: What is the formula for finding the perimeter of a regular polygon?
A: The formula for finding the perimeter of a regular polygon is:
Perimeter = n × s
where n is the number of sides and s is the length of one side.
Q: What is the difference between a convex polygon and a concave polygon?
A: A convex polygon is a polygon with all interior angles less than 180 degrees. A concave polygon is a polygon with at least one interior angle greater than 180 degrees.
Q: What is the formula for finding the area of a concave polygon?
A: The formula for finding the area of a concave polygon is:
Area = (base × height) / 2
Q: What is the formula for finding the perimeter of a concave polygon?
A: The formula for finding the perimeter of a concave polygon is:
Perimeter = a + b + c
where a, b, and c are the lengths of the sides of the polygon.
Conclusion
In this Q&A article, we covered various topics related to polygons and triangles, including the definition of a polygon, the difference between acute and right triangles, the formula for finding the area and perimeter of a triangle, and more. We hope this article has been helpful in clarifying any doubts you may have had about polygons and triangles.
Practice Problems
- What is the sum of the interior angles of a quadrilateral?
- What is the formula for finding the area of a regular pentagon?
- What is the difference between a convex polygon and a concave polygon?
Answer Key
- 360 degrees
- Area = (5 × s^2) / (4 × tan(π/5))
- A convex polygon has all interior angles less than 180 degrees, while a concave polygon has at least one interior angle greater than 180 degrees.
Additional Resources
For more practice problems and resources on polygons and triangles, check out the following links: