geometry

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a large square has sides of 24 units, midpoints of its sides are connected to create a smaller square. what is the area of the smaller square

  • geometry -

    consider each corner: a= 1/2 bh=1/2(1/2*24)(1/2*24)=1/8*24^2
    there are are four of these, area of corner triangles= 4*1/8 *24^2=1/2 24^2

    area smaller= arealarger-areacorners
    = 24^2-1/2 (24^2)= 1/2 24^2

    area of smaller square= 1/2 area of bigger square.

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