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WSP Isosceles Triangle Area

  • Isosceles Triangle Area

    Grade: 6th to 8th

    Explore when an isosceles triangle obtains its maximum area.

    This interactive is optimized for your desktop and tablet.

    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

    How to Use

    • You can modify the length of the base by dragging Points A or C.
    • You will not be able to modify the length of the congruent sides, which is fixed to 5 cm.
    • As you modify the length of the base, observe the trace, which shows the relationship between the area of Triangle ABC, and the length of its base, Segment BC.

    Buttons

    • Erase Traces will erase any traces that have been marked on the grid.

     

    Exploration

    • When does Triangle ABC obtain its maximum area?
    • What is the relationship between its sides?
    • What is the relationship between the base and height?
    • Construct a formal or informal proof as to when the maximum area of an isosceles triangle is obtained.
    • Share a scenario where this would be applicable in real life.

     

    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.
    • 6-8
    • Geometry
    • Measurement