The diagonal of the rectangle ABCD is 12 cm and the angle it makes with the side of the CD
| July 11, 2021 | education
The diagonal of the rectangle ABCD is 12 cm and the angle it makes with the side of the CD is 60, find the area of the rectangle.
In a right-angled triangle ACD, the angle CAD = (90 – ACD) = (90 – 60) = 30.
The CD leg lies opposite an angle of 30, then its length is equal to half the length of the AC hypotenuse.
CD = AC / 2 = 12/2 = 6 cm.
By the Pythagorean theorem. Determine the length of the BP leg.
AD ^ 2 = AC ^ 2 – CD ^ 2 = 144 – 36 = 108.
АD = 6 * √3 cm.
Determine the area of the rectangle. Savsd = АD * СD = 6 * √3 * 6 = 36 * √3 cm2.
Answer: The area of the rectangle is 36 * √3 cm2.
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