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Math Help - Area Question...

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    Area Question...

    Prove that the Area of Parallelogram ACC'A' = b^2
    Area Question...-pythagoras.jpg
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  2. #2
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    Quote Originally Posted by MATNTRNG View Post
    Prove that the Area of Parallelogram ACC'A' = b^2
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    If we take it that the triangle with sides a, b, c is right-angled such that a^2+b^2=c^2

    and the inner shape with sides c is a square, then if we label the angle and side as shown in the attachment..
    and the area of the required shape equals the rectangle area,
    we only need calculate kc.

     Cos\theta=\frac{k}{b}\Rightarrow\ k=bCos\theta

    Using the larger triangle... Cos\theta=\frac{b}{c}

    Hence, it's straightforward to calculate kc in terms of b.
    Attached Thumbnails Attached Thumbnails Area Question...-quadrilateralx.jpg  
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