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

Question

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  3\sqrt{3} .

Kudos for a correct  solution .

goldfinchmonster · Answer

The Answer shold be D .

As the question stem states that the given figure is a  parallelogram with equal sides , it can be inferred that the given figure is either a  square  or a  Rhombus .

Statement 1  - As one angle measure is given to be 60, then certainly it is not a square. Hence we are dealing with a Rhombus.
As one angle is 60, the opposite angle will also be 60 and the rest two opposite angles will be 120 each.

Now by dividing the rhombus into two equal triangles ( By drawing diagonals ) we form a 30-30-120 triangle. By using properties of triangle we can deduce the length of the diogonals. This is enough to deduce what question seeks.   Therefore Sufficient.

Statement 2  - It provides with the altitude( therefore again it is a rhombus ), and on substituting this value of altitude in the rhombus, we can derive one angle to be 60. Then it is simmilar to Stmt 1.   Therefore Sufficient.

Temurkhon · Answer

Statement 2 sufficient by itself because provide height, so A=6*3*sqrt3=18*sqrt3. Eliminate A,C,E

Statement 1 says that we have two equilateral triangles with A=6^2*(sqrt*3/4)=9*sqrt3, so 2*9*sqrt3=18*sqrt3. Suff

D

MathRevolution · Answer

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.

saiesta · Answer

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.

ENGRTOMBA2018 · Answer

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 2016-02-02_18-57-28.jpg 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.

bumpbot · Answer

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

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

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