The height of the parallelogram ABCD, drawn from vertex B to side AD
| June 11, 2021 | education
The height of the parallelogram ABCD, drawn from vertex B to side AD, divides it into 3cm and 2cm segments, angle A = 45 degrees. Find the area ABCD.
Let’s define the bottom of the AD.
AD = AH + DH = 3 + 2 = 5 cm.
The height BH forms a right-angled triangle ABH, and since, by condition, the angle BH = 45, this triangle is also isosceles. BH = AH = 3 cm.
Determine the area of the parallelogram.
Savsd = AD * BH = 5 * 3 = 15 cm2.
A variant is possible when AH = 2 cm, and DH = 3 cm, then BH = AH = 2 cm, and Savsd = 5 * 2 = 10 cm2.
Answer: The area of the parallelogram is 15 cm2 or 10 cm2.
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