Question : What is the area of a triangle having a perimeter of 32 cm, one side of 11 cm, and the difference between the other two sides is 5 cm?

Option 1: $8\sqrt{30}$ cm²

Option 2: $5\sqrt{35}$ cm²

Option 3: $6\sqrt{30}$ cm²

Option 4: $8\sqrt{2}$ cm²

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 : The sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 90 cm. Find its area (in cm²).

Option 1: 150

Option 2: 270

Option 3: 30

Option 4: 60

Question : The areas of two similar triangles ABC and PQR are 64 cm² and 144 cm², respectively. If the greatest side of the smaller ΔABC is 24 cm, then what is the greatest side of the bigger ΔPQR?

Option 1: 32 cm

Option 2: 24 cm

Option 3: 42 cm

Option 4: 36 cm

Question : A right-angled isosceles triangle is inscribed in a semi-circle of radius 7 cm. The area enclosed by the semi-circle but exterior to the triangle is:

Option 1: 14 cm²

Option 2: 28 cm²

Option 3: 44 cm²

Option 4: 68 cm²