Area Tool

  • Area Tool

    Grade: 6th to 8th

    Use this tool to determine how the length of the base and the height of a figure can be used to determine its area. Can you find the similarities and differences between the area formulas for trapezoids, parallelograms, and triangles?

    Activity

    Instructions

    • Modes: Investigate trapezoids, parallelograms, and triangles, using the tabs along the top of the frame. Drag the vertices to explore different sizes of each shape.
    • The Add to Table button can be used to record data in the table, which may be useful in trying to identify patterns.
    • The lock button, located at the lower right-hand corner of the interactive, will lock and unlock the height of the polygon. This may be useful in finding the formula for a polygon's area.

    Exploration

    Investigate various sizes for each of the different shapes.
    • What is the formula for finding the area of a trapezoid? How is the length of the mid-line involved in the formula?
    • What is the formula for finding the area of a parallelogram? How is it related to the formula for finding the area of a rectangle?
    • What is the formula for finding the area of a triangle? How is it related to the formula for finding the area of a rectangle?
     

    Objectives and Standards

    NCTM Standards and Expectations
    • Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
    • 6-8
    • Geometry