All GRE Math Resources
Example Questions
Example Question #1 : Quadrilaterals
Find the area of the parallelogram shown above, excluding the interior space occupied by the blue rectangle.
A parallelogram must have two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula:
Additionally, this problem requires you to find the area of the interior rectangle. This can be simply found by applying the formula:
Thus, the solution is:
Example Question #1 : Quadrilaterals
A parallelogram has a base of and a height measurement that is the base length. Find the area of the parallelogram.
Not enough information is provided.
By definition a parallelogram has two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula:
Before applying the formula you must find of .
The solution is:
Note: when working with multiples of ten remove zeros and then tack back onto the product.
There were two total zeros in the factors, so tack on two zeros to the product:
Example Question #2 : Quadrilaterals
Find the area for the parallelogram shown above.
A parallelogram must have two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula:
The solution is:
Example Question #11 : How To Find The Area Of A Parallelogram
A parallelogram has a base of and a height measurement that is the base length. Find the area of the parallelogram.
By definition a parallelogram has two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula:
Before applying the formula you must find of .
The solution is:
Note: when working with multiples of ten remove zeros and then tack back onto the product.
There were two total zeros in the factors, so tack on two zeros to the product:
Example Question #12 : How To Find The Area Of A Parallelogram
ABCD is a rectangle.
Quantity A: The area of AEB
Quantity B: The area BEC
The two quantities are equal.
Quantity B is greater.
Quantity A is greater.
The relationship cannot be determined.
The two quantities are equal.
The area of a triangle is
Consider the rectangle ABCD
As a rectangle:
With appearing directly in the center of the rectangle.
The area of
Notice that the term corresponds to the triangle's height.
The area of
The two quantities are equal.
Example Question #12 : How To Find The Area Of A Parallelogram
Using the parallelogram shown above, find the area.
Not enough information is provided.
This problem provides both the base and height measurements, thus apply the formula:
To find an equivalent answer in inches, you must convert the measurements to inches FIRST, and then multiply:
Therefore, our area in square inches is:
Example Question #1 : How To Find An Angle In A Parallelogram
In a given parallelogram, the measure of one of the interior angles is 25 degrees less than another. What is the approximate measure rounded to the nearest degree of the larger angle?
103 degrees
78 degrees
102 degrees
77 degrees
101 degrees
103 degrees
There are two components to solving this geometry puzzle. First, one must be aware that the sum of the measures of the interior angles of a parallelogram is 360 degrees (sum of the interior angles of a figure = 180(n-2), where n is the number of sides of the figure). Second, one must know that the other two interior angles are doubles of those given here. Thus if we assign one interior angle as x and the other as x-25, we find that x + x + (x-25) + (x-25) = 360. Combining like terms leads to the equation 4x-50=360. Solving for x we find that x = 410/4, 102.5, or approximately 103 degrees. Since x is the measure of the larger angle, this is our answer.
Example Question #2 : How To Find An Angle In A Parallelogram
Figure is a parallelogram.
Quantity A: The largest angle of .
Quantity B:
Which of the following is true?
Quantity B is larger.
The relationship cannot be determined.
Quantity A is larger.
The two quantities are equal.
The two quantities are equal.
By using the properties of parallelograms along with those of supplementary angles, we can rewrite our figure as follows:
Recall, for example, that angle is equal to:
, hence
Now, you know that these angles can all be added up to . You should also know that
Therefore, you can write:
Simplifying, you get:
Now, this means that:
and . Thus, the two values are equal.
Example Question #2 : How To Find An Angle In A Parallelogram
Figure is a parallelogram.
What is in the figure above?
Cannot be computed from the data given.
Because of the character of parallelograms, we know that our figure can be redrawn as follows:
Because it is a four-sided figure, we know that the sum of the angles must be . Thus, we know:
Solving for , we get:
Example Question #1 : How To Find The Length Of The Side Of A Parallelogram
The sum of the two bases in a parallelogram is An adjacent side to the bases is the length of one of the two base measurements. Find the length of one side that is adjacent to the bases.
In this problem, you are told that the sum of the two bases in a parallelogram is Since the two bases must be equivalent, each side must equal: . Additionally, the problem states that the adjacent sides are the length of the bases. Therefore, an adjacent side to the base must equal: