Correct Answer - Option 3 : 19.44 sq cm
Given:
Length of the side of the rhombus is 4.5 cm and diagonal is 5.4 cm
Concept Used:
Area of rhombus = ½ × product of diagonals
Relation between side and diagonals of a rhombus is 4 × (side)2 = (1st diagonal)2 + (2nd diagonal)2
Calculation:
Let, d be the length of the other diagonal
Then,
4 × (4.5)2 = (5.4)2 + d2
⇒ d2 = 4 × 20.25 – 29.16
⇒ d2 = 81 – 29.16
⇒ d = √51.84
⇒ d = 7.2
Area of rhombus = ½ × product of diagonals
⇒ ½ × 5.4 × 7.2
⇒ 38.44/2
⇒ 19.44
∴ The area of the rhombus is 19.44 cm2