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7th Grade Math / Lesson 2: Composite Shapes

What will we be learning in this lesson?

  • In this lesson you will look at how to find the area of a composite shape.
Vocabulary words are found in this purple color throughout the lesson. Remember to put these in your notebook.


  • Some shapes are made up of other basic shapes put together.

  • Look at these shapes:

  • We can break these shapes down into basic shapes to make it easier to find things like their areas.


  • The shape on the left is called a trapezoid. The one on the right is called a hexagon. Let's first look at the trapezoid.


  • If we put two lines into this trapezoid we now have two triangles and a rectangle. These are shapes that we can easily find the areas of. Then we would just need to add the areas of the separate shapes to find the area of the trapezoid.

  • Let's look at an example: Find the area of the trapezoid below. The height is 3 inches.


  • Find the area of the trapezoid below. The height is 3 inches.

    Insert lines to make basic shapes and then find the areas of each shape.
  • The rectangle is the easy part. The top is 4 and the height is 3.
    4 * 3 = 12

  • The triangles have a height of 3 but we need to figure out the bases. The part of the base that is taken up by the rectangle is 4 inches, that leaves 4 inches across the bottom to be split by the two triangles. So each of the bases of the triangles are 2 inches.

    So each of the triangles have an area of
      ½ * 2 * 3 =   ½ * 6 = 3
    The area of the trapezoid is 12 + 3 + 3 = 18


  • Finding the area of a shape that is complex is easier if you can break that shape into smaller, more basic shapes.

  • Always try to break the shape into rectangles, squares, or even triangles so you can find the areas of these basic shapes then add them all together to get the area of the original shape.

  • Can you find the area of a composite shape?
  • Go back to the classroom to get to your homework and any other items you need to attend to.