angle

[ketkoag]

Each side of a certain parallelogram has length 6. if the area of the parallelogram is 18.
which of the following is the measure of one of its angles?
A. 30’ B. 45’ C. 60’ D. 90’ E.120’

OA: A , but if A is the answer then why not E . try to draw a parallelogram with all sides equal and if one angle is 30 then the other angle has to be 120.

[mike22629]

30 + 30 + 120 +120 = 300 (not 360)

Other side would be 150

[m&m]

it say "what is measure of one of the angles". So we know the angles all add to 360 - so if any 2 answers add to 180 then it must be wrong since there would be 2 possible angles choices in the answers.

E & C must then be eliminated
also D cannot be because then we would have a square
so if you had to guess you just made your chances of success 50%

[gauravgundal]

Answer: A
Area of Parallelogram = Base * height
18 = 6 * h
h=3

consider a llm with 6 as side and draw a height of 3
the angle associated with the height and side of 6 is angle 30

[Pranay]

Answer: A
Area of Parallelogram = Base * height
18 = 6 * h
h=3

consider a llm with 6 as side and draw a height of 3
the angle associated with the height and side of 6 is angle 30

Hi Gaurav,

Pranay .. again.

Could you please explain the last step associated with conclusion of angle being 30 degrees.

[hk]

Pranay,

The area of the parallelogram = b*h
18=6*h
h=3

Now drop a line from one of the top edges to the base. you will for a right angle triangle. with h=3, hypotenuse=6 and let x be the other side.

solving we get x=3 Sqrt(3)

This forms a 1:sqrt(3):2 (which have angles 90,60 and 30) triangle and the angle opposite to the smallest side which is 3, is 30' and happens to be one side of the parallelogram. Do not fall into the trap and choose 60 because this just forms a part of the angle. (See diagram)

[ketkoag]

30 + 30 + 120 +120 = 300 (not 360)

Other side would be 150

OMG!! what was i thinking!!!!!
thanks..