In a parallelogram, the smaller diagonal is perpendicular to the side. The height, drawn from a right angle

| April 25, 2021 | education

In a parallelogram, the smaller diagonal is perpendicular to the side. The height, drawn from a right angle, divides the larger side into segments of 64 and 25 cm. Determine the area of the triangle enclosed between the larger side and the diagonals of the parallelogram.

Since, by condition, BD is perpendicular to AB, then triangle ABD is rectangular.

The VN height is drawn from the apex of a right-angled triangle, then by the property of such a height:

BH ^ 2 = AH * D: = 25 * 64 = 160.

BH = 40 cm.

Let’s build the CM height through the point O, the point of intersection of the diagonals. Height KM = BH = 40 cm.

Point O divides the height of KM in half, then OM = KM / 2 = 40/2 = 20 cm.

Determine the area of the triangle AOD.

Saod = AD * ОМ / 2 = (АН + DH) * ОМ / 2 = (25 + 64) * 20/2 = 890 cm2.

Answer: The area of the triangle is 890 cm2.



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