Show that area of rhombus equal to half the product of its diagonal
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Show that area of rhombus equal to half the product of its diagonal
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Answer:
Step-by-step explanation:
I have bunked some steps hope you understand.
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.