In rhombus ABCD AK – bisector of angle CAB, angle BAD = 60 degrees, BK = 12CM. find the area of the rhombus.
| September 17, 2021 | education
The diagonals of the rhombus are the bisectors of the angles at the vertices, then the angle BAO = BAD / 2 = 60/2 = 30. Since, by condition, AK is the bisector of the angle CAB, the angle BAC = 30/2 = 15.
The sum of the adjacent angles of the rhombus is 180 then the angle ABC = 180 – 60 = 120. Then the angle BKA = 180 – 120 – 15 = 45.
In triangle ABK we apply the theorem of sines.
AB / Sin45 = BK / Sin15.
AB = BK * Sin45 / Sin15.
AB = 12 * 0.707 / 0.259 = 32.76 cm.
Determine the area of the rhombus.
S = AB * AD * Sin60 = 32.76 * 32.76 * √3 / 2 = 929.43 cm2.
Answer: The area of the rhombus is 929.43 cm2.
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