IGD Area of a Parallelogram

  • IGD: Area of a Parallelogram

    Grade: 3rd to 5th, 6th to 8th

    How Do You Find the Area of a Parallelogram?

    In a parallelogram, opposite sides are parallel and have the same length. This applet will show you how to divide the parallelogram into pieces, arrange them together to form a rectangle, and then use the formula for the area of a rectangle to find the area of the parallelogram.

    Activity

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    Instructions

    • Drag vertices A and B to change the size and shape of the parallelogram.
    • Drag the red point to move the right half of the parallelogram. Move this piece to create a rectangle with the left half. Click the Make Rectangle box to be shown how a rectangle can be made from the parallelogram.
    • Click the Show Dimensions button to indicate the measurements needed to find the area.
    • The Start Over button resets the diagram.
     

    Exploration

    Change the size and shape of the parallelogram by dragging points A and B. Then, drag the right half of the parallelogram to form a rectangle with the left half.

    • What is the area of the rectangle that you get?
    • Click the Show Dimensions. What measurements of the parallelogram do you need in order to find its area?

    Click the Start Over button, and repeat the investigation for parallelograms of other sizes.

    • Are your conjectures true, regardless of the size of the parallelogram?
    • Do all the parallelograms have the same area?

    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.
    • 3-5
    • 6-8
    • Geometry