Write True or False and justify your answer:If the side of a rhombus i

1.	Write True or False and justify your answer:If the side of a rhombus is 10 cm and one diagonal is 16 cm, then 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.

Write True or False and justify your answer:If the side of a rhombus is 10 cm and one diagonal is 16 cm, then 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.