The diagonal of the rectangle shown divides the rectangle in half creating two right triangles. The legs of the right triangles are congruent to the side lengths of the rectangle. The representation illustrates that the area of each right triangle is half the area of the rectangle. Exploring the decomposition of shapes helps students develop algorithms for determining area of various shapes (e.g., area of a triangle is ½ × base × height). [Graphic cannot be reproduced.]
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The student will estimate and a) measure the distance around a polygon in order to determine its perimeter using U.S. Customary and metric units; and b) count the number of square units needed to cover a given surface in order to determine its area.
Opportunities to explore the concepts of perimeter and area should involve hands-on experiences (e.g., placing toothpicks (units) around a polygon and counting the number of toothpicks to determine its perimeter and filling or covering a polygon with tiles (square units) and counting the tiles to determine its area).
measure the distance around a polygon in order to determine its perimeter using U.S. Customary and metric units; and
count the number of square units needed to cover a given surface in order to determine its area.
Area is the number of iterations of a two-dimensional unit needed to cover a surface. The two-dimensional unit is usually a square, but it could also be another shape such as a rectangle or an equilateral triangle.