Question : Find the area of triangle whose sides are 10 cm, 12 cm, and 18 cm.

Option 1: $22 \sqrt{2} \mathrm{~cm}^2$

Option 2: $30 \sqrt{2} \mathrm{~cm}^2$

Option 3: $28 \sqrt{2} \mathrm{~cm}^2$

Option 4: $40 \sqrt{2} \mathrm{~cm}^2$

Question : Find the area of a triangle whose length of two sides are 4 cm and 5 cm and the angle between them is 45°.

Option 1: $4 \sqrt{2} \mathrm{~cm}^2$

Option 2: $7 \sqrt{2} \mathrm{~cm}^2$

Option 3: $5 \sqrt{2} \mathrm{~cm}^2$

Option 4: $6 \sqrt{2} \mathrm{~cm}^2$

Question : If each side of an equilateral triangle is 12 cm, then its altitude is equal to:

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

Option 2: $3 \sqrt{6}\ \text{cm}$

Option 3: $6 \sqrt{2}\ \text{cm}$

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

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

Question : In a triangle ABC, if $\angle B=90^{\circ}, \angle C=45^{\circ}$ and AC = 4 cm, then the value of BC is:

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

Option 2: $4 \mathrm{~cm}$

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

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