Correct Option: C

Using Rule 12,

Side of a rhombus

=	2p	=	p	unit
	4		2

OA = OC = y (let)
∴ AC = 2y units
OB = OD = x (let)
∴ BD = 2x units
From ∆OAB,
∠AOB = 90°
AB² = OA² + OB²

⇒	p²	= x² + y²
	4

⇒ p² = 4x² + 4y² ...(i)
and 2x + 2y = m
On squaring both sides,
4x² + 4y² + 8xy = m²
⇒ p² + 8xy = m²
⇒ 8xy = m² – p²

⇒ 4xy =	1	(m² + p²)
	2

∴ Area of the rhombus =	1	× AC × BD
	2

=	1	× 2x × 2y =	1	× 4xy
	2		2

=	1	×	1	(m² - p²)
	2		2

=	1	(m² - p²) sq. units
	4