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WSP Area of Triangles

  • Area of Triangles

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

    How Do You Find the Area of a Triangle?

    To find the area of a triangle, find a way to make it look like a shape for which you already know how to find the area. Try to make a parallelogram using a copy of the triangle.

    Activity

     
    Web Sketchpad Copyright © 2015 KCP Technologies, a McGraw-Hill Education Company. All rights reserved.
    Release: 2015Q2, Semantic Version: 4.2.0, Build Number: 911.6-r, Build Stamp: dn.kcptech.com/20150706050244
    Activity Contents Copyright © 2015 National Council of Teachers of Mathematics. All rights reserved.

    Instructions

    The goal is to create a parallelogram by using a copy of any triangle.

    • Change the size and shape of triangle ABC by dragging points A, B, and C.
    • Click the Create Copy button to make a copy of the purple triangle. Translate the yellow copy using point C, and rotate it using point B'.
    • The Construct Parallelogram button will complete the problem for you.
    • The Show Dimensions button indicates the dimensions needed to find the area, and Show Area button will show the area of triangle ABC.
    • The Reset button will allow you to start over.

    Exploration

    Use the Create Copy button to create a yellow copy of the purple triangle. Try to arrange the two triangles to form a parallelogram. If you need help, the Construct Parallelogram button will show one way of making a parallelogram. There are also two other ways—can you find them?

    • What measurements on the triangle do you need to make in order to find the area of a parallelogram?
    • What is the area of the triangle?

    Objectives and Standards

    NCTM Standards and Expectations
    • Geometry / Measurement
    • 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
    • Measurement