Derive Area of Rectangle

Discussion in 'Other Pre-University Math' started by nycmathguy, Jul 7, 2022.

  1. nycmathguy

    nycmathguy

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    Derive the formula A = (width)(length).
     
    nycmathguy, Jul 7, 2022
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  2. nycmathguy

    MathLover1

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    The diagonals of the rectangle divide it into two equivalent right-angled triangles. Therefore, the area of the rectangle will be equal to the sum of the area of these two triangles.
    Suppose, ABCD is a rectangle.

    upload_2022-7-6_22-20-0.jpeg

    Now, let diagonal AC divide the rectangle into two right triangles, i.e. ∆ABC and ∆ADC.

    We know that ∆ABC and ∆ADC are congruent triangles.

    Area of ∆ABC = ½ x base * height = ½ x AB *BC = ½ * b x w

    Area of ∆ADC = ½ *base * height = ½ x CD * AD = ½ *b * w

    Area of rectangle ABCD = Area of ∆ABC + Area of ∆ADC

    Area (ABCD) = 2(½ *b * w)

    Area (ABCD) = l x w

    Thus, the area of the rectangle = Length x Width
     
    MathLover1, Jul 7, 2022
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    nycmathguy likes this.
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  3. nycmathguy

    nycmathguy

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    You definitely know mathematics. God blessed you with this skill. Lucky you.
     
    nycmathguy, Jul 7, 2022
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