How to Compare & Order Shapes By Area: Lesson for Kids

Instructor: Carol PeQueen

Prior to working in a college Elementary Education program, Carol was a 3rd grade teacher. She holds a PhD in Instructional Design.

In this lesson, you will learn how to compare different shapes by area. You will also learn how to arrange shapes in order by how large or small an area they have.

Comparing Shapes By Area

Imagine a new swimming pool is being built at the end of your street, and you get to pick the shape of it! You are allowed three shapes to choose from - rectangle, square, or that shape that looks like the letter 'L.' Now, if you choose the pool that takes up the least amount of area, there will be enough money left over to install a curvy water slide. You want that slide! How will you choose which design has the smallest area?

Three Swimming Pools

Using Congruent Shapes to Measure Area

One way to compare the areas of different shapes is to use congruent shapes - figures that are shaped the same and are exactly the same size. When congruent shapes are laid on top of these different swimming pools, it then becomes much easier to find the area of each one. By this method, you will know for sure which design has the smallest area.

In the swimming pool problem, same-sized squares (shown in purple) could be used as the congruent shape to measure area. By laying the congruent squares on top of the first pool, we see that it takes 25 squares to completely fill the space. Take a minute to see if you can figure out how many purple squares the other two pools would need.

Using congruent squares

Ordering the Shapes

Once all three pools have been measured in this way, we find that the rectangle pool fits 21 purple squares and the L-shaped pool fits only 20 purple squares. And as we already know, the square pool fits 25 purple squares. Once we have our areas, we simply order them from largest to smallest:

  • The square pool fits 25 purple squares.
  • The rectangle pool fits 21 purple squares.
  • The L-shaped pool fits 20 purple squares.

So, the L-shaped pool has the smallest area of all three designs and will allow you to add that curvy water slide!

Could we have selected a different size square in the beginning as our standard for measuring the area of the pools? Yes, but only if all the squares we are using are all the same size. Remember, the shapes used to measure area have to be congruent.

Did we have to use a square as our shape? No. Other shapes can be used to measure area. For example, triangles could have been used to measure the area, as long as the triangles are congruent - all exactly the same type of triangle, and all exactly the same size.

Congruent triangles can be used as a tool for comparing area, too.
Using Triangles Instead

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