Question

proof of area of parallelogram equal (b x h)
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Answer 1

Answer:

The formula is A = b x h and it is really simple to prove. If we cut a triangle off of one end of a parallelogram and move it to the other end, we get a RECTANGLE, whose area is the same as the based of the parallelogram times its height.

Answer 2

Let ABCDABCD be the parallelogram whose area is being sought.

Let FF be the foot of the altitude from CC

Also label a point EE such that DEDE is the altitudefrom DD (see figure above).

Extend ABAB to FF.

Then:

ADAD≅≅BCBC∠AED∠AED≅≅∠BFC∠BFCDEDE≅≅CFCF

Thus:

△AED≅△BFC⟹(AED)=(BFC)△AED≅△BFC⟹(AED)=(BFC)

So:

(ABCD)=EF⋅FC=AB⋅CF(ABCD)=EF⋅FC=AB⋅CF

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