Question

Find the area of a rhombus whose perimeter is 260cm and the length of one of its diagonal is 66cm.

Answer 1

The perimeter of the Rhombus = 260cm

Each side of the Rhombus = `(1)/(4)(260)` = 65cm

In the given, Rhombus, AB = 65cm, diagonal AC = 66cm
We know that, diagonals of a Rhombus bisect at right angles.
In Triangle AOB,
∠AOB = 90°, AB is the hypotensue

AO = `33"cm"(1/2 (66"cm"))`

AB² = OB² + OA²
⇒ OB 
= `sqrt("AB"^2 - "OA"^2)`
= `sqrt(65^2 - 33^2)`
= `sqrt(4225 - 1089)`
= `sqrt(3136)`
= 56
⇒ AB = 112cm
We know that the area of a rhombus whose diagonals are d₁ and d₂, is

A = `(1)/(2) xx "d"_1 xx "d"_2`

∴ the area of a rhombus whose diagonals are 112 and 66, is

A = `(1)/(2) xx 112 xx 66`
= 3696cm².