Prove that the area of parellelograms is the product of any its sides and the corresponding altitudes .

please provide the whole proof !!!!!!

Question

Prove that the area of parellelograms is the product of any its
sides and the corresponding altitudes
please provide the whole proof !!!!!!

Ajanta Trivedi · Accepted Answer

given: let ABCD be a parallelogram and AE be the altitude from A to side DC TPT ; area(parallelogram ABCD)=CD*AE construction: join AC and from C draw an altitude to AB proof: area(ABCD)=area(Î”ADC)+area(Î”ABC) $= \frac{1}{2} * C D * A E + \frac{1}{2} * A B * C F = \frac{1}{2} * C D * A E + \frac{1}{2} * C D * A E [∵ C F = A E]$ the distance between two parallel lines is always constant and AB=CD [opposite sides of a parallelogram are equal] therefore area(ABCD)=CD*AE i e area of parallelogram is the product of its one side and corresponding altitude

Prove that the area of parellelograms is the product of any its sides and the corresponding altitudes . please provide the whole proof !!!!!!

Prove that the area of parellelograms is the product of any its sides and the corresponding altitudes .

please provide the whole proof !!!!!!