An equilateral triangular sheet is formed by joining 9 equilateral triangular sheets each of area 9\sqrt{3} \text{cm}^2. What is the height of the bigger triangular sheet?

Explanation

Total area = 9 \times 9\sqrt{3} = 81\sqrt{3} \text{cm}^2. The area of the larger equilateral triangle with side A is \frac{\sqrt{3}}{4}A^2 = 81\sqrt{3} \implies A^2 = 324 \implies A = 18 cm. Its height is \frac{\sqrt{3}}{2}A = \frac{\sqrt{3}}{2}(18) = 9\sqrt{3} cm.

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