Question

Let ABCD be a parallelogram such that AB = 10 , BC = 14, and Angle A = 45. Find the area of the parallelogram.

Answer 1

Answer:

Area of a parallelogram is base times height. Note that CD = AB & AD = BC

to find the height, draw a line from angle B perpendicular to the base b. Lets call the point of intersection at the base E. This constitutes a right triangle with AB as the hypotenuse. Using the law of sine to calculate the height h:

h/sin(A) = AB/sin(90°) ( sin(90°) = 1)

h = AB * sin(45°)

h = 10 * sin(45°)

Area = 14 * 10 * sin(45°) = 140 * sin(45°) ≈ 98.99 QEDexplanation: