Question

Prove that the area of a rhombus=1/2*product of the diagonls.

Answer 1

aloha!

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Prove that the area of a rhombus=1/2*product of the diagonals.

proof: we know that area of triangle = half × base × height
         

also, the diagonals of a rhombus make 90° angle with each other forming four right angled triangles.
now,
area of ABCD = ar AOD + ar AOB + ar OCD + ar OCB
area of ABCD = 1/2×DO×AO+1/2×OB×AO+1/2×OD×OC+1/2×OB×OC
area of ABCD = 1/2×AO { DO + OB } + 1/2×OC { OD + OB }
area of ABCD = 1/2×AO { DB } + 1/2×OC { DB }
area of ABCD = 1/2×DB { AO + OC }

area of ABCD = 1/2×DB×AC.

{ here DB and AC are the diagonals }

so, hence proved.

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hope it helps :)