In rectangle abcd, the bisector of angle A meets BC at point E. Find the area of the rectangle if BE = 4 cm, BC = 4.5 cm.
| March 5, 2021 | education
In a rectangle, all interior angles are 90, and since AE is the bisector of the angle, the angle BAE = DAE = 45.
The angle DАЕ = АЕВ as the cross-lying angles at the intersection of parallel lines ВС and АD of the secant АЕ, then the angle BAE = BEA = 45, and therefore the triangle ABE is rectangular and isosceles. AB = BE = 4 cm.
Let’s define the area of the rectangle ABCD.
Savsd = AB * BC = 4 * 4.5 = 18 cm2.
Answer: The area of the rectangle is 18 cm2.
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