Q. 54.2( 5 Votes )

If the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of the rhombus is 96 cm2

Answer :

To find the area of rhombus, we divide it into two triangles.

As all the sides of a rhombus are equal, we have for a triangle


a = 10, b = 10, c = 16


s = (a + b + c)/2


s = (10 + 10 + 16)/2 = 36/2 = 18.


Area(Δ) = √s(s-a)(s-b)(s-c)


Area(Δ) = √18(18-10)(18-10)(18-16)


Area(Δ) = √18×8×8×2


Area(Δ) = 48cm2


As the sides of the other triangle are also same, so their areas will also be equal.


Area(Rhombus) = Area(Δ) + Area(Δ)


Area(Rhombus) = 48 + 48 = 96cm2


Hence, the statement is True.


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