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S=\frac{1}{2}\times 2\sqrt{3}\sqrt{5}\sqrt{3}
Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.
S=\frac{1}{2}\times 2\times 3\sqrt{5}
Multiply \sqrt{3} and \sqrt{3} to get 3.
S=3\sqrt{5}
Cancel out 2 and 2.