Let ABCD be the rhombus. Diagonals AC and BD intersect at point E.
l(AC) = 48 cm …(i)
l(AE) = \(\cfrac{1}{2}\)l(AC)…[Diagonals of a rhombus bisect each other]
=\(\cfrac{1}{2}\) × 48 …[From (i)]
= 24 cm …(ii)
Perimeter of rhombus = 100 cm …[Given]
Perimeter of rhombus = 4 × side
∴ 100 = 4 × l(AD)
∴ l(AD) = \(\cfrac{100}{4}\) = 25 cm …(iii)
In ∆ADE,
m∠AED = 90° …[Diagonals of a rhombus are perpendicular to each other]
∴ The area of the quadrilateral is 336 sq.cm.
