The length of each side of a regular hexagon is 12 cm. The length of one of the diagonals of a rhombus whose area is equal to √3 times the area of the hexagon is 72 cm. What is the length (in cm) of the other diagonal of the rhombus? Option 1: 16 Option 2: 18 Option 3: 15 Option 4: 24

Answer: 18. Solution: Area of a regular hexagon with side 12 cm is 3√3/2(12)^2=216√3 square cm. The area of the rhombus is √3 times the area of the hexagon: 216√3x√3=648 If the rhombus diagonals are 72 cm and d cm: 1/2x72x d=648 36d=648 d=18 cm.

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The length of each side of a regular hexagon is 12 cm. The length of one of the diagonals of a rhombus whose area is equal to $\sqrt{3}$ times the area of the hexagon is 72 cm. What is the length (in cm) of the other diagonal of the rhombus?

✅ Correct Option: 2

Area of a regular hexagon with side 12 cm is $\dfrac{3\sqrt{3}}{2}(12)^2=216\sqrt{3}$ square cm. The area of the rhombus is $\sqrt{3}$ times the area of the hexagon: $216\sqrt{3}\times\sqrt{3}=648$ If the rhombus diagonals are 72 cm and $d$ cm: $\dfrac{1}{2}\times72\times d=648$ $36d=648$ $d=18$ cm.

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The length of each side of a regular hexagon is 12 cm. The length of one of the diagonals of a rhombus whose area is equal to $\sqrt{3}$ times the area of the hexagon is 72 cm. What is the length (in cm) of the other diagonal of the rhombus?

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