The lengths of one side of a rhombus and one of the two diagonals are 6 cm each. The area of the rhombus (in cm$$^2)$$ is:​

Correct option is C

​Given:
- Side of rhombus (s) = 6 cm
- One diagonal (d₁) = 6 cm
Formula Used:
Area of rhombus = $$(\frac{1}{2}) × d₁ × d₂$$​
Using Pythagoras theorem to find the other diagonal d₂:
Each half of diagonal d₁ = $$\frac{d₁}{2}$$ = 3 cm 

$$s² = (\frac{d₁}{2})² + (\frac{d₂}{2})² \\\ \\=> \frac{d₂}{2} = \sqrt{(s² - (\frac{d₁}{2})²)}$$​​

Solution:

$$\frac{d₂}{2}:$$

$$\frac{d₂}{2} = \sqrt{(6² - 3²)} = \sqrt{(36 - 9)} = √27 = 3√3 cm$$​​
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Therefore, d₂ = 2 × 3√3 = 6√3 cm
Area = $$(\frac{1}{2}) × 6 × 6√3 = 3 × 6√3$$​ = 18√3 cm²

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