Question : The area of an equilateral triangle is $4 \sqrt{3} \mathrm{~cm}^2$. Find the side (in cm) of the triangle.

Option 1: $2$

Option 2: $4$

Option 3: $\sqrt{3}$

Option 4: $2 \sqrt{3}$

Question : The sides of a triangle are 8 cm, 12 cm, and 16 cm. What is the area of the triangle?

Option 1: $24 \sqrt{15}~\text{cm}^2$

Option 2: $6 \sqrt{15}~\text{cm}^2$

Option 3: $8 \sqrt{15}~\text{cm}^2$

Option 4: $12 \sqrt{15}~\text{cm}^2$

Question : In triangle ABC which is equilateral. O is the point of intersection of altitude AL, BM, and CN. If OA = 16 cm, what is the semi-perimeter of the triangle ABC?

Option 1: $8 \sqrt 3$ cm

Option 2: $12 \sqrt 3$ cm

Option 3: $16 \sqrt 3$ cm

Option 4: $24\sqrt 3$ cm

Question : The altitude of an equilateral triangle of side $\frac{2}{\sqrt3}$ cm is:

Option 1: $\frac{4}{3}$ cm

Option 2: $\frac{4}{\sqrt3}$ cm

Option 3: $\frac{2}{3}$ cm 

Option 4: $1$ cm

Question : The length of each side of an equilateral triangle is $14 \sqrt{3}$ cm. The area of the incircle (in cm²), is:

Option 1: 450

Option 2: 308

Option 3: 154

Option 4: 77