# Regular and Irregular Polygons

Laney

Created on September 23, 2024

Students will learn the difference between regular and irregular polygons and how to find the perimeter and area of both.

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## Transcript

of Regular Polygons

Area

High School Geometry

Start!

Contents

Homepage

Introduction

Task

Process

Resources

Evaluation

Conclusion

Students start here!

Credits

Intro

Grade Level: High School GeometryContact Info: Laney Gilbertlgilbert13@sycamores.indstate.edu

Description

Standards

Indiana Content Standards covered:G.QP.4: Compute perimeters and areas of regular and irregular polygons to solve real-world and other mathematical problems.

This webquest teaches students how to find area and perimeter of regular and irregular polygons and connects the processes to real-world scenarios.

Homepage

Back to Contents

What's a regular polypon? What about an irregular polygon?

Introduction

Take notes on the new vocabulary terms you learn along the way and write down any examples that are worked out along with the questions at the end. Your notes and worked out examples will be collected for a grade when you're finished.

Next

Back to Contents

Review

Need a little review on area first?

If you'd like a quick refresher on how to find the area of rectangles and triangles and where the formulas come from, please watch this video. If you feel confident in these things, you may move on to the next slide.

Back to Contents

Previous

Next

Regular vs. Irregular

Watch the video to the right that explains the difference between regular and irregular polygons. Feel free to take notes as the video progresses. Once you've finished the video, click the buttons below and complete the questions.

apply

reflect

Next

Back to Contents

Previous

Review: Area & Perimeter

1

What's the area of the rectangle?

9 units2

12 units2

7 units2

Next

Back to Contents

Previous

Review: Area & Perimeter

2

What's the area of the triangle?

10 units2

3 units2

6 units2

Next

Back to Contents

Previous

Take a look at the shape below. How do you think we could find the area using what you know about area and polygons?

Show strategies

This is a paragraph of text waiting to be awesome content

Count boxes

Split into multipleshapes

Use a formula

Next

Previous

Back to Contents

Task

What would the area of this regular pentagon be? Let's find out!

5 cm

7 cm

Next

Previous

Back to Contents

Process

Apothem

A=1/2(aP)

Perimeter

Click on the items below to lean more about them. Then, complete the example.

Example

Back to Contents

Previous

Next

Video Tutorial

How are polygons and their areas used in our everyday lives?

Formula and an example

Back to Contents

Previous

Next

Here is a video of two examples worked out if you need to see more examples.

This is a short article explaining what the apothem and area formula are, and a worked out example.

Here are some examples of regular polygons in our lives!

Resources

Question 1

Using what you learned, find the area of this regular pentagon. Round to the nearest square cm.

5 cm

7 cm

Next

Previous

Back to Contents

Record your answer on your paper.

Question 2

Now try this example. If you need a hint, click the "hint" button to the left of the octagon. Round to the nearest square centimeter.

5 cm

Next

Previous

Back to Contents

Hint

Record your answer on your paper.

5.3cm

2.1cm

}

Evaluation

You will receive credit for the vocab terms and examples if they are written down correctly. For questions 1 & 2, you will receive half a point for the correct answer and the other half for using a logical method and showing your work.This assignment is out of 5 points.

This is how your assignment will be scored.

Previous

Back to Contents

Next

The difference between a regular and irregular polygon

The definition of an apothem

How to find the area of a regular polygon given the apothem and a side length

Here are the things you learned today

Great job, you finished your WebQuest!

This is a quick sneak peek into some future material we will be learning. Later, we will look at finding area of irregular polygons and finding area of regular polygons given different parts of the polygon.

Back to Contents

Previous

Credits

YouTube Videos:

Area review: https://www.youtube.com/watch?v=iRWR6jEi6cQ

Intro to regular and irregular polygons: https://www.youtube.com/watch?v=UN57vvrMrY4

Video Tutorial: https://www.youtube.com/watch?v=CXeAeGwaLzY

Webpages:

Area formula and example: https://www.varsitytutors.com/hotmath/hotmath_help/topics/areas-of-regular-polygons

Examples of polygons in everyday life: https://unacademy.com/content/cat/study-material/mathematics/polygons-are-used-in-daily-life-situations/

Back to Contents

The perimeter of a regular polygon can be found by multiplying the number of sides by one of the side lengths.

3cm

Take this octagon for example. Since it's regular, all the side lengths are the same. Therefore, the perimeter equals 8x3, or 24 cm.

This approach can work, but won't be the most accurate because we have to estimate the partial boxes. Is there a way that will get us a more precise answer?

Reminder: The area of a rectangle can be found by either multiplying the length and width or by counting the squares inside the shape (if on graph paper).

A formula would be nice, but what would it be??

- Plan the structure of your communication.
- Give it a hierarchy and give visual weight to the main point.
- Add secondary messages with interactivity.
- Establish a flow through the content.
- Measure results.

Contextualize your topic

Opportunities

Let's start with a shape that will be easy to check our answer.

4cm

8cm

Find the area of the square pictured above. Use the new formula first, then check your answer using the area formula for a square.

Need Help?

1. What's the length of the apothem?2. Find the perimeter.3. Use A=1/2(aP) where a=length of apothem and P=perimeter

Reminder: The area of a triangle can be found by multiplying the base and height and dividing it by 2.

The apothem is a perpendicular line from the center of a polygon to the center of one of its sides. It is labelled as 'a'.

Reminder: The area of a rectangle can be found by either multiplying the length and width or by counting the squares inside the shape (if on graph paper).

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Remember: The apothem goes from the center of the shape to the midpoint of a side. Therefore, the halves of the side that the apothem intersects are equal.

The formula for finding the area of a regular polygon given its apothem and side length isA=1/2(aP), where a is the length of the apothem and P is the shape's perimeter.

Reminder: The area of a triangle can be found by multiplying the base and height and dividing it by 2.

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Great job!!

This approach will work if we remember the area formulas for a triangle and a trapezoid... but what if we don't remember these? Do we really want to split every polygon into more shapes to find their areas?

Great job!!