Interesting Cube Problem

If the cube has a volume of 64, what is the area of the green parallelogram? (Assume points I and J are midpoints.)

Go ahead, work it out. Then, go here for a more in depth discussion, including a video explanation. Also, see my very simple solution in the comments on that page. (My Precalculus students should especially take note!)

And, welcome, SAT Math Blog, to the internet! Thanks for pointing us to this great problem and creating the nice diagram above.

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3 thoughts on “Interesting Cube Problem

  1. I read in one of your posts that you’re interested in jsxgraph. You might be interested to know that I rendered that cube and rhombus using jsxgraph. It was a bit tedious but it got the job done.

    var b = JXG.JSXGraph.initBoard(‘jxgbox’, {axis:false, boundingbox:[-2,-2,8,8]});

    var p1 = b.createElement(‘point’,[0,0], {name:’A’,style:4});
    var p2 = b.createElement(‘point’,[2,0], {name:’B’,style:4});
    var p3 = b.createElement(‘point’,[2,2], {name:’C’,style:4});
    var p4 = b.createElement(‘point’,[0,2], {name:’D’,style:4});

    var p5 = b.createElement(‘point’,[-1.4,1.4], {name:’E’,style:4});
    var p6 = b.createElement(‘point’,[.6,1.4],{name:’F’,style:4});
    var p7 = b.createElement(‘point’,[.6,3.4], {name:’G’,style:4});
    var p8 = b.createElement(‘point’,[-1.4,3.4], {name:’H’,style:4});

    var p9 = b.createElement(‘line’,[p1,p5],{straightFirst:false, straightLast:false});
    var p10 = b.createElement(‘line’,[p2,p6],{straightFirst:false, straightLast:false});
    var p11 = b.createElement(‘line’,[p3,p7],{straightFirst:false, straightLast:false});
    var p12 = b.createElement(‘line’,[p4,p8],{straightFirst:false, straightLast:false});

    var p13 = b.createElement(‘point’,[-1.4,2.4],{name:’I’,style:4});
    var p14 = b.createElement(‘point’,[2,1],{name:’J’,style:4});

    var poly = b.createElement(‘polygon’,[p1,p2,p3,p4],{fillOpacity:0});
    var poly2 = b.createElement(‘polygon’,[p5,p6,p7,p8],{fillOpacity:0});
    var poly3 = b.createElement(‘polygon’,[p1,p13,p7,p14],{fillOpacity:7});

    Sol

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