# Perimeters and Areas of Similar Rectangles Investigation

I love giving my students hands-on activities whenever I can. Hands-on activities help students understand the relationships between different geometric properties. I try to make my area and volume unit as hands-on as possible. I love doing this hands-on activity when I'm teaching about the area of rectangles, parallelograms, and trapezoids. I also like this activity for helping students figure out the formula for the area of a circle.

Perimeters and areas of similar figures has always been a little bit of a struggle for my students. I think one of the reasons is because it's the very last lesson of the year that I teach. However, I wanted to make sure that my students had the opportunity to remember the lesson.

This activity would work well for students to do alone or with a partner. It also works well as a demo on the board for students to watch. For this activity, you need graph paper. That's it! If you don't have graph paper, you can also do this activity with plain paper and a ruler.  I recommend measuring with centimeters because inches might get too big. However, not all students have the best measuring skills, so that could mess up the activity.

## Perimeters and Areas of Similar Rectangles Investigation

First, draw a 3 by 4 unit rectangle. Label it "Original". Then, draw four more similar rectangles and label them "I", "II", "III", and "IV".

Then, use the drawings to find the perimeter and area of each rectangle. Students will have different sized rectangles, so they will have different areas and perimeters. Don't worry about it.

Next, find the ratio of the areas and perimeters and the similarity ratio (scale factor).

Then, it's discussion time! Have students compare the ratios of the perimeters with the similarity ratio. What do they notice? Then, compare the ratio of the areas with the similarity ratio. What do they notice?

If students have completed their own investigation on their own graph paper, it would be great for them to include this in their interactive notebooks! Having students put this on the page facing the "official" notes about similar figures would be a perfect way for students to remember the lesson as soon as they glance at the page.

If you would like a copy of the recording worksheet, click HERE. It's a PDF. Some computers say that there is an error with the file, but if you download it anyway there shouldn't be a problem.