A polygon that can be divided into more than one basic figure is said to be a composite figure (or shape). Students should understand how to divide a polygon into familiar figures using concrete materials (e.g., pattern blocks, tangrams, geoboards, grid paper, paper (folding), etc.). [Graphic cannot be reproduced.] This diagonal of the rectangle above subdivides the rectangle in half and creates two right triangles. The figure can also be formed by combining two right triangles that are congruent. The resulting figure shows that the legs of the right triangles are congruent to the sides of the rectangle. The representation illustrates that the area of each right triangle is half the area of the rectangle. Exploring decomposition of shapes helps students develop algorithms for determining area of various shapes (e.g., area of a triangle is ½ × base × height).
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