Areas of More Complex Shapes
In this lesson, students build on strategies developed in the earlier geoboard area activities. Here's a shape to try to find the area of, along with a few strategies that might be used by students:
Use one small geoboard square
as the unit of area.
One way is to subdivide the area into smaller parts:
Another way is to look at what's not inside the trapezoid shape:
A third way is to rearrange the parts and then find the area:
The area determined by all three methods is the same!
Sometimes, one method will work better than another one, depending on the shape itself. Here are some examples to work on - which methods work best for you?
We also do some more exploring with changing the unit of area, and determining the effect on the area of the shape. Here is a shape and a variety of area units. Give it a try!
Can you see a relationship
between the change in the size
of the area unit and the measured
area of the shape?
I hope you had fun with these! Area relationships are one of the fundamental building blocks of geometry, so lots of exploration is important. Talk with your child about the areas you can see in the world around you. Talk as well about what kinds of units are appropriate for measuring various areas. For instance, it might be easier to talk about a football field in terms of square yards rather than square inches or centimeters!