In rectangle ABCD, the diagonal is 5 cm and makes an angle of 60 degrees with side AB
| September 26, 2021 | education
In rectangle ABCD, the diagonal is 5 cm and makes an angle of 60 degrees with side AB. Find the area of the given rectangle.
In a right-angled triangle ABC, the angle ACB = (180 – ABC – BAC) = (180 – 90 – 60) = 30.
The AB leg is located opposite an angle of 300, then its length is equal to half the length of the AC diagonal.
AB = AC / 2 = 5/2 = 2.5 cm.
In a right-angled triangle ABC, according to the Pythagorean theorem, we determine the length of the leg BC.
BC ^ 2 = AC ^ 2 – AB ^ 2 = 5 ^ 2 – (5/2) ^ 2 = 25 – 25/4 = 75/4.
BC = 5 * √3 / 2 cm.
Determine the area of the rectangle AVSD.
Savsd = AB * BC = (5/2) * (5 * √3 / 2) = 25 * √3 / 4 = 6.25 * √3 cm2.
Answer: The area of the rectangle is 6.25 * √3 cm2.
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