ABCD – parallelogram, O – intersection point of its diagonals. Find the area of a parallelogram

| June 23, 2021 | education

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

By the property of the diagonal of the parallelogram, we make the statement that the diagonal BC divides the parallelogram ABCD into two equal triangles: ABC and ACD. Accordingly, the area of the parallelogram will be equal to the sum of the areas of two equal triangles.
Consider a triangle ABC, in which BО is the median (a property of the diagonals of a parallelogram). The median BО divided the triangle ABC into two triangles having the same area (property of the median of the triangle).
S ABO = S BCO = 7.5 (cm²).
S ABC = 2 * S ABO = 15 (cm²).
S ABCD = 2 * S ABC = 2 * 15 = 30 (cm²).
Answer: The area of the parallelogram ABCD is 30 cm².



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