Area of Polygons Practice

After the students learned the area of triangles, parallelograms, and trapezoids, they needed to practice.

It would be easy to give them a worksheet with the shapes on it and all the measurements given and they just have to plug the numbers into the formula the solve.

Worksheets can be useful, but when there is a way to not do a worksheet, do it.

I did this activity last year and wish I would have saved all the shapes I made. So I remade them again and laminated them.

I drew 10-12 triangles, parallelograms, and trapezoids each. I spread them around the room and asked the students to find the area of the shapes. They measured everything to the nearest centimeters.

To make them talk to each other about it, I asked them to verify their answers with their classmates. I put a large poster at the front of the room with a table of the shapes. Once students have verified their answers with 3 other classmates, they could start adding the area of the shapes to the poster.

Once I made and laminated all the shapes, the activity was easy to put together. I didn't even use any copies! Just notebook paper.

If you dont want to draw your own shapes, you can use this file here. Download it for free. 

Here is another way for students to practice finding the area of polygons fro my TpT store. 

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In Texas, 6th graders are to "determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers." 

Decomposing a Trapezoid--Finding the Area

This has been one of my most favorite and wonderful lessons of my entire teaching career. My students pleasant surprised me with how awesome they are.

Students need to be able to explain how shapes can be decomposed into other shapes to find the area--that is how the formulas are derived.

There are several different ways trapezoids can be decomposed and rearranged to make other shapes. Before this lesson, the students had a guided lesson to decompose parallelograms to rectangles and triangles to parallelograms. So they had previous experience with cutting and rearranging shapes.

I wanted to see if they could take what they had done and apply it to trapezoids.

And they did awesome.

I gave them a sheet of trapeziods and a ruler. I asked them to pick any trapezoid and find a way to decompose it, rearrange it, and find the area.

My advanced class found 8 different ways to find the area. My on-level class found 5 different ways.

I don't have the list we made in front of me, but these are some of the ones I remember they were able to find.

• Cut the trapezoid by the diagonal to make two triangles
• Cut off two triangles at the ends to make one square and one rectangle
• Cut off one triangle and you have a triangle and a rectangle (When one of the sides of the trapezoid is also the height
• Cut the trapezoid by the height, rearrange and make a rectangle
• Double the trapezoid to make a parallelogram
• Cut off one triangle, add to the other side to make a rectangle

After the students spent some time exploring, I had students share what they found. We looked at the measurements of the original trapezoids and of the new shapes they created and found some patterns.

Sometimes, the new base was in between the two original bases(specifically it was the average of the two bases). When you had a triangle, you used the formula 1/2bh and added to the area of the other piece. If you doubled the trapezoid, you would have to half the area of your new shape. 

The last step was to write a formula that they could use to find the area of a trapezoid so they wouldn't have to decompose a trapezoid every time they wanted to find the area. I'll need to improve this part of the lesson. Students got the adding something, the multiplying the height and either multiplying by 1/2 or dividing by 2, just not in a way that would work. 

It was a fun lesson and I was walking around so excited all day long because they were doing such a good job trying and finding ways to decompose the trapezoids!

If you want pdf of the printable with the trapezoids, you can download it here. 

If you want some notebook pages that show decomposing shapes to find the area, I have some in my store.