rhombus

Question

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45

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+1427

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.

blackpanther Dec 3, 2023

parmen · Answer 1 · 2023-12-03T01:49:36

Let h be the length of the altitude from C to AB.

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