Question

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

Options

• True

• False

Answer 1

This statement is True.

Explanation:

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) = `sqrt(s(s - a)(s - b)(s - c))`

⇒ Area (Δ) = `sqrt(18(18 - 10)(18 - 10)(18 - 16))`

⇒ Area (Δ) = `sqrt(18 xx 8 xx 8 xx 2)`

⇒ Area (Δ) = 48 cm²

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 = 96 cm²