Question

show that area of rombus is half the productthe length of its diagonals
if u answer my question i will mark as brain list
*(in 30 min)
date:26-1-19(current)
time:11:55(current)
fast...

Answer 1

Answer:

Hence Proved! See the answer...

Step-by-step explanation:

Given: A rhombus ABCD with its diagonals AC and BD intersecting at O.

To Prove: Area of rhombus ABCD = 1/2 * AC * BD

Proof:

(See the attachment for the figure.)

We know that the diagonals of rhombus bisect each other at 90°

Thus, DO is perpendicular to AC and OB is also perpendicular to AC.

Now, Area of triangle ADC = 1/2 * AC * DO

And, Area of triangle ABC = 1/2 * AC * BO

_____________________________

Area of rhombus ABCD = Area of triangle ABC + Area of triangle ADC

= 1/2 * AC * BO + 1/2 * AC * DO

Taking out common 1/2 * AC,

Area of ABCD = 1/2 * AC * (BO + DO)

But, BO + DO = BD.

Thus, Area of rhombus ABCD = 1/2 * AC * BD