The area of the parallelogram ABCD is 120. Point E is the midpoint of the CD side.
| August 16, 2021 | education
The area of the parallelogram ABCD is 120. Point E is the midpoint of the CD side. Go trapezium square AВED
From point E, the middle of the side СD, draw a line ЕН parallel to the sides ВС and АD of the parallelogram.
The EH segment divides the parallelogram ABCD into two equal parallelograms, then Saned = S nvse = Savsd / 2 = 120/2 = 60 cm2.
The quadrilateral НВСО is a parallelogram, since all its sides are parallel, and the segment BE is its diagonal, which divides it into two equal triangles.
Snve = Svall = Snvse / 2 = 60/2 = 30 cm2.
Then the area of the trapezoid ABED is equal to: Sаvse = Saned + Sнve = 60 + 30 = 90 cm2.
Answer: The area of the ABED trapezoid is 90 cm2.
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