Question

show that the area of a rhombus is half the product of its diagonals

Answer 1

let ABCD be a Rhombus whose diagonals are AC and BD.
then,
area of Rhombus ABCD
=area of triangle ABD + area of triangle BCD
=1/2×base×height + 1/2×base×height
=1/2×BD×AO + 1/2×BD×OC
since diagonals of rhombus are perpendicular to each other
=BD(AO+OC)/2
=BD×AC/2