The diagonal of rectangle ABCD is 20. The angle between the diagonals is 45 degrees. Find the area of the ABO triangle.
| September 22, 2021 | education
Since ABCD is a rectangle, its diagonals are equal and are divided in half at the point of their intersection.
AC = BD = 20 cm.
AO = ОВ = OC = ОD = АС / 2 = 20/2 = 10 cm.
In the triangle AOB, the angle AOB, by condition, is equal to 45, AO = OB = 10 cm.
Determine the area of the triangle ABO.
Savo = AO * BO * SinAOB / 2 = 10 * 10 * Sin45 / 2 = 100 * (√2 / 2) / 2 = 25 * √2 cm2.
Answer: The area of the ABO triangle is 25 * √2 cm2.
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