Question : ABCDEF is a regular hexagon. The side of the hexagon is 36 cm. What is the area of the $\triangle ABC$?

Option 1: $324 \sqrt{3}\ {cm}^2$

Option 2: $360 \sqrt{3} \ {cm}^2$

Option 3: $240 \sqrt{3} \ {cm}^2$

Option 4: $192 \sqrt{3} \ {cm}^2$

Question : The height of an equilateral triangle is $7 \sqrt{3}$ cm. What is the area of this equilateral triangle?

Option 1: $36 \sqrt{3}$ cm²

Option 2: $25 \sqrt{3}$ cm²

Option 3: $49 \sqrt{3}$ cm²

Option 4: $32 \sqrt{3}$ cm²

Question : In the given figure, ABCDEF is a regular hexagon whose side is 6 cm. APF, QAB, DCR, and DES are equilateral triangles. What is the area (in cm²) of the shaded region?

Option 1: $24\sqrt{3}$

Option 2: $18\sqrt{3}$

Option 3: $72\sqrt{3}$

Option 4: $36\sqrt{3}$

Question : A pyramid has an equilateral triangle as its base, of which each side is 8 cm. Its slant edge is 24 cm. The whole surface area of the pyramid (in cm²) is:

Option 1: $(16 \sqrt{3}+24 \sqrt{35})$

Option 2: $(12 \sqrt{3}+24 \sqrt{35})$

Option 3: $(24\sqrt{3}+36\sqrt{35})$

Option 4: $(16\sqrt{3}+48\sqrt{35})$

Question : The base of a right prism is an equilateral triangle whose side is 10 cm. If the height of this prism is $10 \sqrt{3}$ cm, then what is the total surface area of the prism?

Option 1: $125 \sqrt{3}$ cm²

Option 2: $325 \sqrt{3}$ cm²

Option 3: $150 \sqrt{3}$ cm²

Option 4: $350 \sqrt{3}$ cm²