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

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 ratio of three sides of a triangle is $5: 5: 8$. If the area of triangle is $12\;\mathrm{cm^2}$, then what is the length (in$\;\mathrm{cm}$) of the equal sides?

Option 1: 5

Option 2: 8

Option 3: 6

Option 4: 2.5

Question : If the area of an equilateral triangle is $a$ and height $b$, then the value of $\frac{b^2}{a}$ is:

Option 1: $3$

Option 2: $\frac{1}{3}$

Option 3: $\sqrt3$

Option 4: $\frac{1}{\sqrt3}$

Question : ABCD is a square. Draw an equilateral $\triangle $PBC on side BC considering BC is a base and an equilateral $\triangle $QAC on diagonal AC considering AC is a base. Find the value of $\frac{\text{area of $\triangle PBC$}}{\text{area of $\triangle QAC$}}$.

Option 1: $\frac{1}{2}$

Option 2: $1$

Option 3: $\frac{1}{3}$

Option 4: $\frac{1}{4}$