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…
Question and options
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 times the area of the hexagon is 72 cm. What is the length (in cm) of the other diagonal of the rhombus?
- 16
- 18
- 15
- 24
Answer and explanation
Correct answer: B - 18
Hexagon area = (3sqrt(3)/2) x 144 = 216sqrt(3). The rhombus area is sqrt(3) times that, i.e. 648, so d1 x d2/2 = 648 and d2 = 1296/72 = 18.
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