Question

The diagonals of a rhombus are 18 cm and 24 cm. Find:
(i) its area ;
(ii) length of its sides.
(iii) its perimeter

Answer 1

The diagonal of the rhombus is 18 cm and 24 cm.
area of rhombus = `1/2` x Product of diagonals
= `1/2` x 18 x 24
= 216 cm²

(ii)

Diagonals of a rhombus bisect each other at right angles.

∴ OA = `1/2 xx 24 = 12` cm

OB = `1/2 xx 18 = 9` cm

In right ∠d Δ AOB

AB = `sqrt("OA"^2 + "OB"^2)`

= `sqrt((12)^2 + (9)^2)`

= `sqrt(144 + 81)`

= `sqrt(225) = 15` cm

∴ Side of rhombus = 15 cm

(iii)

Perimeter of rhombus = `4 xx "side"`

= `4 xx 15 = 60` cm

(i) 216 cm² (ii) 15 cm (iii) 60 cm.