Question

prove that the area of a triangle is half the product of any its sides and the corresponding altitudes

Answer 1

Heya,

Answer to your question is:-


CONSTRUCTION:
Through C and A draw CP parallel to BA and AP parallel to BC, intersecting each other at P.

PROOF:
CP parallel to BA  (By Construction)

AP parallel to BC  (By Construction)

Therefore BCPA is a parallelogram.

Hence AC is a diagonal of parallelogram BCPA.

Therefore,
area of triangle = ½ ar(IIgm BCPA) = ½ × BC × AD  (As BC is the base and AD is the altitude of IIgm BCPA).

Hence, Proved!

HOPE THIS HELPS YOU:-))
@Ashu

Answer 2

....HOPE IT WILL HELP YOU....