The area of a parallelogram is the product of its base and the corresponding altitude. GIVEN : A parallelogram `A B C D` in which `A B` is the base and `A L` the corresponding altitude. TO PROVE : `a r(^(gm)A B C D)=A BxA L` CONSTRUCTION : Complete the rectangle `A L M B` by drawing `B M_|_C Ddot`

Explanation

`"Let ABCD be the parallelogram and BL the altitude corresponding to the side AB"`

`"Complete the rectangle ABLM"`

`"Parallelogram ABCD and rectangle ABLM are on the same base and between the same parallels AB and MC"`

`therefore ar(ABCD) = ar(ABLM)`

`=>ar(ABCD) = AB xx BL->"(area of a rectangle " = "length"xx"breadth)"`

`"Hence, the area of a parallelogram is the product of any base of it and the corresponding altitude"`