Derive Area of Triangle

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

  1. nycmathguy

    nycmathguy

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    Derive the formula A = (1/2)(base)(height).
     
    nycmathguy, Jul 7, 2022
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  2. nycmathguy

    MathLover1

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    A good way to start off with the proof of the area of a triangle is to use the area of a rectangle to quickly derive the area of a right triangle.
    Start with a rectangle ABCD and let h be the height and b be the base as shown below:
    [​IMG]

    The area of this rectangle is b × h
    However, if we draw a diagonal from one vertex, it will break the rectangle into two congruent or equal triangles.

    [​IMG]
    The area of each triangle is half the area of the rectangle. For example, the area of triangle ABC is 1/2(b × h). Does that make sense?
     
    MathLover1, Jul 7, 2022
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  3. nycmathguy

    nycmathguy

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    Perfect. How do you draw geometric shapes?
     
    nycmathguy, Jul 7, 2022
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