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In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $20^\circ.$  Find the area of the rhombus.

 Dec 3, 2023
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Let h be the length of the altitude from C to AB.

 

Since ∠BCO=20∘, △BCO is a 30-60-90 triangle. Therefore, BC=3​CO​=3​h​=43​.

 

Since all the side lengths in the rhombus are equal to 12, we have that AB=43​. Therefore, the area of the rhombus is 21​⋅AB⋅h=21​⋅43​⋅43​=48​.

 Dec 3, 2023

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