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Application of Theorem (Triangle and Parallelogram on Same Base )

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Computing the area of a triangle


The area of a triangle can be demonstrated as half of the area of a parallelogram which has the same base length and height.

Calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is:

where b is the length of the base of the triangle, and h is the height or altitude of the triangle. (Our solved example in mathguru.com uses this concept)

The term 'base' denotes any side and 'height' denotes the length of a perpendicular from the vertex opposite the side onto the line containing the side itself.




Area formulas


The area of the parallelogram is the area of the blue region, which is the interior of the parallelogram

§  The area of the parallelogram to the right (the blue area) is the total area of the rectangle less the area of the two orange triangles.

The area of the rectangle is

and the area of a single orange triangle is

Therefore, the area of the parallelogram is

(Our solved example in mathguru.com uses this concept)




The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.


(Our solved example in mathguru.com also uses the below concept. This is our own explanation, it is not taken from Wikipedia.)

If a Triangle and Parallelogram are on the same base and between the same parallel lines, then area of triangle is equal to half the area of parallelogram.