Question : An incircle with center O is drawn inside an equilateral triangle ABC and the length of the side is 12 cm. Find the area (in sq cm) of the triangle which is not in the incircle.

Option 1: 24.67

Option 2: 21.48

Option 3: 37.71

Option 4: 30.64

Question : $\triangle$ABC is similar to $\triangle$PQR. The length of AB is 16 cm and the length of the corresponding side PQ is 9 cm. If the area of $\triangle$ABC is 1024 sq. cm, what is the area of $\triangle$PQR?

Option 1: 768 sq. cm

Option 2: 32 sq. cm

Option 3: 324 sq. cm

Option 4: 128 sq. cm

Question : The length of each side of an equilateral triangle is 22 cm. Find the area (in cm²) of this triangle.

Option 1: 121

Option 2: $242 \sqrt{3}$

Option 3: $121 \sqrt{3}$

Option 4: 242

Question : Two triangles MNO and XYZ are given similar with the ratio of their side as 9 : 4. If the area of the larger triangle is 243 sq. cm, then the area of the smaller triangle will be:

Option 1: 162 sq. cm

Option 2: 28 sq. cm

Option 3: 48 sq. cm

Option 4: 16 sq. cm

Question : In the isosceles triangle ABC with BC is the unequal side of the triangle, and line AD is the median drawn from the vertex A to the side BC. If the length AC = 5 cm and the length of the median is 4 cm, then find the length of BC (in (cm).

Option 1: 5

Option 2: 3

Option 3: 4

Option 4: 6

Question : In an equilateral triangle ABC, P is the centroid of this triangle. Side of $\triangle A B C$ is $16 \sqrt{3} \ \text{cm}$. What is the distance of point P from side BC?

Option 1: 8 cm

Option 2: 12 cm

Option 3: 9 cm

Option 4: 10 cm