Question : The side of an equilateral triangle is 12 cm. What is the radius of the circle circumscribing this equilateral triangle?

Option 1: $6 \sqrt{3}\ \text{cm}$

Option 2: $4\sqrt{3}\ \text{cm}$

Option 3: $9 \sqrt{3}\ \text{cm}$

Option 4: $5\sqrt{3}\ \text{cm}$

Question : What is the altitude of an equilateral triangle whose side is 15 cm?

Option 1: $15\sqrt3\text{ cm}$

Option 2: $10\sqrt 3\text{ cm}$

Option 3: $\frac{9\sqrt 3 }{2}\text{ cm}$

Option 4: $\frac{15\sqrt 3}{2}\text{ cm}$

Question : The side of an equilateral triangle is 9 cm. What is the radius of the circle circumscribing this equilateral triangle?

Option 1: $2\sqrt{3}$ cm

Option 2: $5\sqrt{3}$ cm

Option 3: $4\sqrt{3}$ cm

Option 4: $3\sqrt{3}$ cm

Question : The centroid of an equilateral triangle PQR is L. If PQ = 6 cm, the length of PL is:

Option 1: $2 \sqrt{3}\ \text{cm}$

Option 2: $4 \sqrt{3}\ \text{cm}$

Option 3: $5 \sqrt{3}\ \text{cm}$

Option 4: $3 \sqrt{3}\ \text{cm}$

Question : The height of an equilateral triangle is $9 \sqrt{3} \mathrm{~cm}$. What is the area of this equilateral triangle?

Option 1:  $92 \sqrt{3} \mathrm{~cm}^2$

Option 2: $67 \sqrt{3} \mathrm{~cm}^2$

Option 3: $49 \sqrt{3} \mathrm{~cm}^2$

Option 4: $81 \sqrt{3} \mathrm{~cm}^2$