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Using Tiling to Find Area

3.MD.7
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Aligned To Common Core Standard:

Grade 3 Measurement - 3.MD.7

How to determine the area of a shape by breaking it into smaller parts? Calculating the area of regular two-dimensional shapes is easy. You need dimensions of one side in case of a square, two sides for a rectangle and a triangle, and the radius in case of a circle. As you proceed further in mensuration, you will come across shapes that are not that straightforward and are made of different shapes. These shapes are called composite shapes. As there are area formulae for the basic two-dimensional shapes such as square, rectangle, triangle, and circle, the area of these composite shapes can become difficult to calculate. There is one way you can do that, and it is through breaking composite shapes into smaller parts. To understand the process, let us take this example; Do you recognize this shape? Well, this is a composite shape that is made of various other two-dimensional shapes. Here is how we can break this composite shape into smaller parts; These are the three ways you can break this composite shape. As this shape does not contain any curved boundaries, breaking into a circle is not possible. You can now calculate the area for each small part and sum the areas of all the small parts to get the area of the composite shape. These worksheets help students learn how to find the area of unique shapes and figures.

Printable Worksheets And Lessons


  • Tiling Area Step-by-step Lesson- Things start to break in pieces, to help us find the area of shapes.

  • Guided Lesson - More practice on this skill. This skill is often over looked and under taught.

  • Guided Lesson Explanation - I think I did a pretty good job breaking this one down for you.

  • Practice Worksheet - We drill and kill it, but I added a literal twist to the shape three times. I saw this stump kids on the last test even though it is the same exact skill.

  • Matching Worksheet - Match the rectangles to the length of their sides.


Homework Sheets

Breaking large squares into smaller squares is a huge leap in geometry at this age.

  • Homework 1- Break the rectangle into 4 equal pieces by drawing and labeling the length of all four pieces. Calculate the area before and after you break it apart.
  • Homework 2- Divide the rectangle into 4 equal pieces by drawing and labeling the length of all four pieces. Calculate the area before and after splitting it apart.
  • Homework 3- Divide the rectangle into 4 equal pieces by drawing and labeling the length of all four pieces. Calculate the area before and after splitting it apart.



Practice Worksheets

Taking these rectangles apart piece-by-piece is an interesting way to go about it.

  • Practice 1- Divide the rectangle into 4 equal pieces by drawing and labeling the length of all four pieces. Calculate the area before and after splitting it apart.
  • Practice 2- Break the rectangle into 4 equal pieces by drawing and labeling the length of all four pieces. Calculate the area before and after you break it apart.
  • Practice 3- Divide the rectangle into 4 equal pieces by drawing and labeling the length of all four pieces. Calculate the area before and after splitting it apart.



Math Skill Quizzes

The same skills are tested here, just in a different format.

  • Quiz 1- The pieces below are one piece of four piece rectangle. Determine the length of the sides of the large rectangle based on the measures for the pieces below.
  • Quiz 2- The pieces below are one piece of four piece rectangle. Determine the length of the sides of the large rectangle based on the measures for the pieces below.
  • Quiz 3