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Derive the formula A = (1/2)(base)(height).
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:
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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.
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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?