Question

Find the area of a rhombus, whose one side and one diagonal measure 20cm and 24cm respectively.

Answer 1

In the given Rhombus diagonal AC = 24cm.

We know that, diagonals of a Rhombus bisect at right angles. In Triangle AOB.
∠AOB = 90°, AB is the hypotenuse

AO = `12"cm"(1/2 (24"cm"))`

AB² = OB²  +OA²
⇒ OB 
= `sqrt("AB"^2 - "OA"^2)`
= `sqrt(20^2 - 12^2)`
= `sqrt(400 - 144)`
= `sqrt(256)`
= 16
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 24 and 32 is,

A = `(1)/(2) xx 24 xx 32`
= 384cm².