A class set of composite figures made up of tangram shapes

• Model the concept of a composite figure using a familiar drawing such as the floor plan of a house with an attached garage. The basic shape of the house can be a rectangle and the garage can be a square.

  

• Tell students they are to determine the area of the house plan shown. Ask students how they would begin to solve the problem. They should tell you that the figure needs to be broken into polygonal parts. The polygons that make up the figure will be rectangles and/or triangles. These are polygons whose area formulas have been developed.

  

• Then use some of the composite figures from tangrams (described in the clarification example) and have the students determine the polygons' dimensions using the dimension of the small triangle.

  

• Model how you would structure the problem before allowing students to find the area. Elicit from them the steps that need to occur before they can determine the area of the composite figure. Many students will find they understand the concept perfectly, but will make a mistake in organizing the problem on paper.

  • Label/number each figure that makes up the composite figure.

  • Label the dimensions of the sides needed to find the area of each figure with the measure determined using the side of the small triangle.

    

  • Determine the area of each figure that makes up the composite figure.
• Now have students find the total area of the composite figure by adding the area of all the polygons. Basic polygons can be used for this activity, but tangram pieces are all related so that all you have to do is provide one dimension of one figure to find the dimensions of all the other figures.
• Each student can then make a tangram drawing that resembles an object. They should remove the shared line segments. Students will then calculate the areas of each other's composite figures.