In rectangle ABCD, the diagonal BD makes an angle of 30 degrees with the side CD
| September 10, 2021 | education
In rectangle ABCD, the diagonal BD makes an angle of 30 degrees with the side CD and is equal to 22 cm. Find Sabcd.
Let’s draw a diagonal AC, which are divided in half at point O, then OD = OC = 22/2 = 11 cm.
Angle ОDА = 90 – 30 = 60. Then triangle AOD is equilateral and the angle between the diagonals is 60.
Then Savsd = (АС * ВD * Sin60) / 2 = (22 * 22 * √3 / 2) / 2 = 121 * √3 cm2.
Answer: The area of the rectangle is 121 * √3 cm2.
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