If each side of a parallelogram has a length of 6, what is the area of

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If each side of a parallelogram has a length of 6, what is the area of the parallelogram?

(1) One angle of the parallelogram measures 60 degrees.
(2) The altitude of the parallelogram is 33 √ .

Geometric DS questions do not need to be solved complicatedly. If the 4 sides are of the same length it is a rhombus, which we need to know length of one side and the length of a diagonal; there are 2 variables and one equation as we know one side is equal to 6.
The number of equation needs to match that of the variables, and there 2 equations are given from the 2 conditions, so the answer becomes (D).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

Care to elaborate? What is the rule/property of a 30-30-120 triangle. I know the rules of the 30-60-90 triangle and 45-45-90 triangle.

No need to go into the 30-30-120 triangle (this triangle is infact a combination of 2 30-60-90 degree triangles). Refer to the attached image.

Area of this paralellogram (or any parallelogram for that matter) = base X height = AB*DE . You are already given AB = 6



Per statement 1, \(\angle{DAE} = 60\) ---> makes triangle DAE a right angled 30-60-90 triangle with right angle at E. You are also given AD. Thus, you can easily calculate DE. Hence sufficient to calculate the area of the parallelogram.

Per statement 2, this statement directly gives the value of DE. Hence sufficient.

D is thus the correct answer.

Hope this helps.

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