ABCD is a parallelogram, O is the point of intersection of its diagonals.

| May 26, 2021 | education

ABCD is a parallelogram, O is the point of intersection of its diagonals. Find the area of the parallelogram if the area of the ABO triangle is 7.5 cm2

The diagonal BD divides the parallelogram into two equal triangles, since the bases of the triangles ABD and BCD are equal to BC = BD and the total height. Then Svd = Svsd.

The diagonals of the parallelogram, at the point of intersection, are divided in half, then the segment AO, for the triangle ABD is the median of the triangle, OB = OD.

According to the property of the median of a triangle, it divides it into two equal triangles SАо = Sada = 7.5 cm.

Similarly, Svos = Ssod, then the parallelogram area will be equal to: Savsd = 4 * Savo = 4 * 7.5 = 30 cm2.

Answer: The area of the parallelogram is 30 cm2.



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