Question

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

Answer 1

Hey !!

Here is your answer.⬇⬇

Proff :- let ◻ABCD is rhombus. AC and BD are two diagonals.

So, Area of ◻ ABCD = Area of ∆ABD + Area of ∆CBD

=( BD × AO )/2 + ( BD × OC )/2
.....( As we know that diagonals of rhombus are perpendicular to each other )

= BD/2 (AO + OC)
= ( BD × AC )/2 ......( AO + OC = AC )
= 1/2 × length of its diagonals. ..... ( proved )



HOPE IT HELPS YOU....

THANKS ^-^