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 cm^{2}

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) = 48cm^{2}

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 = 96cm^{2}

Hence, the statement is True.

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