The diagonals of a rhombus are 48 cm and 20 cm long. Find (i) the area of the rhombus and (ii) the perimeter of the rhombus.

Explanation

(i) Area of the given rhombus
`=((1)/(2) xx "product of diagonals")`
`=((1)/(2) xx 48 xx 20)cm^(2) = 480 cm^(2)`.
(ii) We know that the diagonals of a rhombus bisect each other at right angles.
`therefore" "OA = OC = 24 cm, OB = OD = 10 cm and angle AOB = 90^(@)`.
By Pythagoras' theorem, we have
`AB = sqrt(OA^(2) + OB^(2))=sqrt((24)^(2)+(10)^(2))` cm
`= sqrt(676)`cm = 26 cm.
`therefore" ""perimeter of the rhombus" = (4 xx 26) cm = 104 cm`.