Question

Show that area of rhombus equal to half the product of its diagonal

Answer 1

Answer:

Step-by-step explanation:

I have bunked some steps hope you understand.

Answer 2

Suppose ABCD is a rhombus.

Now, according to the characteristics of a rhombus,

AB = BC = CD = DA

<AOB = <BOC = <COD <DOA= 90°................( < = angle )........equation 1.

Now, in triangle ABC,

Base (b) = BC

Height (h) = BO.........( by equation 1)

So, area of ABC = 1/2 × b × h

=BO× AC / 2

Samely, area of triangle CDA

= AC×OD / 2

Now, Area of rhimbus = ar(ABC) +
ar(CDA)

= BO × AC / 2 + OD × AC / 2

= AC × ( BO + OD ) / 2

= AC×BD / 2.......●

Hence Proved...●

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Hope it was helpful.