Find the area of a rhombus whose perimeter is 164 cm and one diagonal is of length 80 cm.

Correct option is C

Given:
Perimeter of the rhombus = 164 cm
One diagonal (d₁) = 80 cm
Concept Used:
All sides of a rhombus are equal.
Diagonals bisect each other at right angles.
Area of a rhombus = $$\frac 12$$​ × d₁ × d₂
Side = $$\frac{\text{Perimeter}}{4}$$​​
Solution:
Side =$$\frac{164}{4}$$​ = 41 cm
Half of d₁ = $$\frac{80}{2}$$​= 40 cm
Using Pythagoras Theorem:
​$$41^2 = 40^2 + \left(\frac{d_2}{2}\right)^2 \\\Rightarrow 1681 = 1600 + \left(\frac{d_2}{2}\right)^2 \\\Rightarrow \left(\frac{d_2}{2}\right)^2 = 81 \\\Rightarrow \frac{d_2}{2} = 9 \\\Rightarrow d_2 = 18 \, \text{cm}$$​​
Area = $$\frac{1}{2}$$​ × 80 × 18 = 720 cm²
The area of the rhombus is 720 cm².