How to construct regular polygons using a ruler and a protractor

Colleen Mckinnon

19 Sept 201602:24

Summary

TLDRThis instructional script outlines the process of constructing a regular pentagon with a 15 cm perimeter. It begins by calculating the side length as 3 cm, followed by determining the interior angle using the formula (n-2) * 180 / n, yielding 108 degrees for a pentagon. The tutorial then guides through measuring and marking the first side, using a protractor to draw 108-degree angles, and ensuring accuracy by aligning the paper to the angle and stopping at 3 cm for consistent side lengths. The final step involves connecting the dots to form the pentagon, with a tolerance of ±2 mm.

Takeaways

📏 To construct a regular pentagon, a ruler and a protractor are essential tools.
📐 The perimeter of the pentagon is given as 15 centimeters, which is divided by 5 to find the side length of 3 centimeters each.
🔢 The formula for calculating the interior angle of a regular polygon is (n - 2) * 180 / n, where n is the number of sides.
🤔 For a pentagon, the interior angle is calculated as (5 - 2) * 180 / 5, resulting in 108 degrees.
📝 It's important to show all steps in the construction process to achieve full marks.
📐 Use a ruler to measure and draw the first side of 3 centimeters.
📐 With a protractor, measure 108 degrees from the edge of the first side to mark the next vertex.
📐 Ensure the paper is rotated correctly to maintain the 108-degree angle while marking subsequent vertices.
📐 The last side should close the shape, forming a regular pentagon, with a slight margin of error allowed (±2 millimeters).
🔄 Accuracy in the final side is critical as it determines the overall shape of the pentagon.
📐 The process involves repeating the steps of measuring and marking at 108 degrees until the pentagon is complete.
🎨 The final product is a regular pentagon with 108-degree interior angles and 3-centimeter sides.

Q & A

What tools are required to construct a regular pentagon as described in the script?
-A ruler and a protractor are required to construct a regular pentagon.
What is the perimeter of the pentagon that the script describes?
-The perimeter of the pentagon is 15 centimeters.
How is the side length of the pentagon calculated?
-The side length is calculated by dividing the total perimeter by the number of sides, which is 15 centimeters divided by 5, resulting in 3 centimeters per side.
What formula is used to find the interior angle of a regular polygon?
-The formula used to find the interior angle of a regular polygon is (n - 2) * 180 / n, where n is the number of sides.
What is the interior angle of the pentagon constructed in the script?
-The interior angle of the pentagon is 108 degrees.
How is the first side of the pentagon measured?
-The first side is measured using a ruler to mark off 3 centimeters.
What step follows measuring the first side in the construction process?
-After measuring the first side, a protractor is used to measure out 108 degrees from the edge of the side and mark it with a dot.
Why is it important to ensure all sides are the same length in a regular polygon?
-Ensuring all sides are the same length is crucial for maintaining the regularity and symmetry of the polygon.
What is the final step described in the script for completing the pentagon?
-The final step is to close the shape by connecting the last point to the starting point, ensuring the side is approximately 3 centimeters.
What is the tolerance level for accuracy mentioned in the script?
-The tolerance level for accuracy is plus or minus two millimeters.
Why is it not necessary to use the protractor for the last side in the script's method?
-It is not necessary to use the protractor for the last side because the shape can be closed by aligning the final point with the starting point, ensuring the regularity of the pentagon.

Outlines

00:00

📏 Constructing a Regular Pentagon

This paragraph provides a step-by-step guide on how to construct a regular pentagon with a perimeter of 15 centimeters. It begins by calculating the side length, which is 3 centimeters, by dividing the total perimeter by the number of sides (5). The interior angle of a regular polygon is found using the formula (n-2) * 180 / n, where n is the number of sides. For a pentagon, this results in an interior angle of 108 degrees. The process involves using a ruler to measure and draw each side and a protractor to mark off the correct angles. The construction requires careful measurement to ensure that all sides are equal and that the angles are accurate. The final step is to connect the dots, ensuring that the last side closes the shape at the correct length, resulting in a regular pentagon with 108-degree interior angles and 3-centimeter sides, with an acceptable margin of error of plus or minus two millimeters.

Mindmap

Keywords

💡Regular Polygon

A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). In the video script, the main theme revolves around constructing a regular polygon, specifically a pentagon, which is a type of regular polygon with five sides. The script details the process of calculating side lengths and interior angles to ensure the polygon is regular.

💡Pentagon

A pentagon is a five-sided figure and is the specific type of regular polygon being constructed in the video. The script provides a step-by-step guide on how to create a pentagon with a perimeter of 15 centimeters, emphasizing the importance of equal side lengths and angles for it to be considered regular.

💡Perimeter

The perimeter is the total length around a shape, which is calculated by adding up the lengths of all its sides. In the context of the video, the perimeter of the pentagon is given as 15 centimeters, and this value is used to determine the length of each side of the pentagon.

💡Side Length

The side length refers to the measurement of one side of a polygon. In the script, the side length of the pentagon is calculated by dividing the total perimeter by the number of sides, resulting in each side being 3 centimeters long.

💡Interior Angle

The interior angle of a polygon is the angle formed between two adjacent sides at a vertex. The script explains the formula for calculating the interior angle of a regular polygon, which is used to determine that each interior angle of the pentagon is 108 degrees.

💡Formula

In mathematics, a formula is an equation that uses variables to express a relationship between different quantities. The script mentions a specific formula for calculating the interior angles of a regular polygon, which is (n - 2) * 180 / n, where 'n' is the number of sides.

💡Protractor

A protractor is a tool used to measure angles. In the script, a protractor is essential for marking the correct 108-degree angles when constructing the pentagon, ensuring that all interior angles are equal.

💡Ruler

A ruler is a measuring instrument used to measure length. The script instructs the use of a ruler to measure and draw the 3-centimeter sides of the pentagon, maintaining the equilateral property of the polygon.

💡Accuracy

Accuracy refers to the closeness of a measured or calculated value to the true or actual value. The script mentions that the accuracy of the constructed pentagon will depend on the last side measured and that a slight deviation of plus or minus two millimeters is acceptable.

💡Construction

In geometry, construction refers to the process of drawing or creating a geometric figure according to certain rules or steps. The video script outlines the construction process of a regular pentagon, detailing each step from calculating dimensions to marking and drawing the shape.

💡Dot

In the context of the script, a dot is used to mark a point on the paper where the 108-degree angle is to be drawn. It serves as a reference point for the construction process, ensuring that the angles are correctly measured and drawn.

Highlights

Introduction to constructing a regular pentagon with specific tools like a ruler and a protractor.

Determination of the side length for the pentagon using the perimeter formula, resulting in 3 centimeters per side.

Explanation of the importance of knowing the interior angle for constructing a regular polygon.

Use of the formula \( n - 2 \times 180 \) / \( n \) to calculate the interior angle of a polygon.

Application of the formula to find the interior angle of a pentagon, which is 108 degrees.

Demonstration of measuring the first side of the pentagon using a ruler.

Instructions on using a protractor to measure the 108-degree angle from the edge of the first side.

Technique of marking the angle and ensuring the paper is aligned to maintain accuracy.

Method of stopping at 3 centimeters to ensure all sides are equal in length.

Continuation of the process by repeating the 108-degree angle measurement for subsequent sides.

Emphasis on the accuracy of the last side in determining the overall shape of the pentagon.

Alternative method of closing the shape without using the protractor for the final side.

Verification of the pentagon's shape by ensuring the last side is approximately 3 centimeters.

Tolerance level mentioned for the construction, allowing a deviation of plus or minus two millimeters.

Completion of the regular pentagon with 108-degree interior angles and 3-centimeter sides.