The diagonal of the parallelogram ABCD is perpendicular to the AD side.
| May 24, 2021 | education
The diagonal of the parallelogram ABCD is perpendicular to the AD side. find the area of the parallelogram ABCD if AB = 12 cm angle B = 41 degrees sin41 ^ = 0.6561 cos 41 ^ = 0.7547
Consider a right-angled triangle ABC, which, by condition, has an angle C of a straight line, and an angle B = 41.
Then Sin41 = AC / AB.
AC = AB * Sin41 = 12 * 0.6561 = 7.8732 cm.
Cos410 = BC / AB.
BC = AB * Cos41 = 12 * 0.7547 = 9.0564 cm.
Then the area of the parallelogram is:
Savsd = AC * BC = 7.8732 * 9.9564 = 71.3 cm2.
Answer: The area of the parallelogram is 71.3 cm2.
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