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The area of a triangle is half the product of its base b and its height h.
A=1/2bh
The triangle's base can be any of its sides. The height – or altitude – of the triangle is the segment that is perpendicular to the base and connects the base or its extension with its opposite vertex.
First, consider the particular case of a right triangle. It is always possible to reflect a right triangle across its hypotenuse to form a rectangle.
Note that the area of the rectangle formed is twice the area of the original right triangle. Because of this, the formula for the area of the rectangle, A_r=l w, can be used to find the area of the right triangle. A_r = 2A_t ⇒ l w = 2A_t Furthermore, the height and base of the right triangle have the same measures as the width and length of the rectangle formed by reflecting the triangle. Based on this observation, b and h can be substituted for l and w, respectively, to solve for the area of the original right triangle in terms of its base and height.
This shows that the area of a right triangle can be calculated by using the formula A = 12bh.
To generalize the previous result, it is useful to note that any non-right triangle can be split into two right triangles by drawing one of its heights.
Note that the area of the non-right triangle A is equal to the sum of the individual areas of the smaller right triangles A_1 and A_2. Therefore, it is possible to calculate the area of the non-right triangle by using the previous result for the areas of the smaller right triangles.
Add fractions
Factor out h
a/b=1/b* a
b_1+b_2= b
It has been found that the area of the non-right triangle is half the product of its base b and its height h. This is the same result as the area for a right triangle. Therefore, the area of any triangle is half the product of its base b and its height h.
A = 1/2bh