Parallelograms - GRE Quantitative Reasoning
Card 1 of 232
ABCD is a rectangle.
Quantity A: The area of AEB
Quantity B: The area BEC
ABCD is a rectangle.
Quantity A: The area of AEB
Quantity B: The area BEC
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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.
The area of a triangle is
Consider the rectangle ABCD
As a rectangle:
With
The area of
Notice that the
The area of
The two quantities are equal.
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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?
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?
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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.
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.
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Figure 
is a parallelogram.
What is 
in the figure above?
Figure
What is
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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:
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
Solving for
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Figure 
is a parallelogram.
Quantity A: The largest angle of 
.
Quantity B: 
Which of the following is true?
Figure
Quantity A: The largest angle of
Quantity B:
Which of the following is true?
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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.
By using the properties of parallelograms along with those of supplementary angles, we can rewrite our figure as follows:
Recall, for example, that angle
Now, you know that these angles can all be added up to
Therefore, you can write:
Simplifying, you get:
Now, this means that:
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A parallelogram has a base of 
and a height of 
. Find the area of the parallelogram.
A parallelogram has a base of
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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:
The solution is:
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:
The solution is:
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A parallelogram has a base of 
and a height measurement that is 
the base length. Find the area of the parallelogram.
A parallelogram has a base of
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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 final solution is:
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
The final solution is:
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Using the parallelogram shown above, find the area.
Using the parallelogram shown above, find the area.
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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:
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:
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A parallelogram has a base of 
and a height of 
. Find the area of the parallelogram.
A parallelogram has a base of
Tap to reveal answer
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:
The solution is:
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:
The solution is:
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A parallelogram has a base of 
and a height measurement that is 
the base length. Find the area of the parallelogram.
A parallelogram has a base of
Tap to reveal answer
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:
Before applying the formula you must find 
of 
.
The solution is:
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:
Before applying the formula you must find
The solution is:
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Using the parallelogram shown above, find the area.
Using the parallelogram shown above, find the area.
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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:
The solution is:
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:
The solution is:
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A parallelogram has a base of 
meters and a height measurement that is 
the base length. Find the area of the parallelogram.
A parallelogram has a base of
Tap to reveal answer
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:
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
The solution is:
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A parallelogram has a base of 
and a height of 
. Find the area of the parallelogram.
A parallelogram has a base of
Tap to reveal answer
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:
Note: prior to applying the formula, the answer choices require you to be able to convert 
to 
, as well as 
to 
. Or, you could have converted the mixed numbers to improper fractions and then multiplied the two terms:
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:
Note: prior to applying the formula, the answer choices require you to be able to convert
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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.
The sum of the two bases in a parallelogram is
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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:
In this problem, you are told that the sum of the two bases in a parallelogram is
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Find the area of the parallelogram shown above, excluding the interior space occupied by the blue rectangle.
Find the area of the parallelogram shown above, excluding the interior space occupied by the blue rectangle.
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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:
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:
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A parallelogram has a base of 
and a height measurement that is 
the base length. Find the area of the parallelogram.
A parallelogram has a base of
Tap to reveal answer
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:
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
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:
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Find the area for the parallelogram shown above.
Find the area for the parallelogram shown above.
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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:
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:
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A parallelogram has a base of 
and a height measurement that is 
the base length. Find the area of the parallelogram.
A parallelogram has a base of
Tap to reveal answer
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:
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
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:
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A parallelogram has a base of 
. The perimeter of the parallelogram is 
. Find the length of an adjacent side to the base.
A parallelogram has a base of
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A parallelogram must have two sets of congruent/parallel opposite sides. Therefore, this parallelogram must have two sides with a measurement of 
and two base sides each with a length of 
Since the perimeter and one base length is provided in the question, work backwards using the perimeter formula:
, where 
and 
are the measurements of adjacent sides.
Thus, the solution is:
Check:
A parallelogram must have two sets of congruent/parallel opposite sides. Therefore, this parallelogram must have two sides with a measurement of
Thus, the solution is:
Check:
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Using the parallelogram shown above, find thesum of the two sides adjacent to the base.
Using the parallelogram shown above, find thesum of the two sides adjacent to the base.
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To find one of the adjacent sides to the base, first note that the interior triangles represented by the red vertical lines must have a height of 
and a base length of 
Then, apply the formula: 
to find the length of one side.
Thus, the solution is:
Therefore, the sum of the two sides is:
To find one of the adjacent sides to the base, first note that the interior triangles represented by the red vertical lines must have a height of
Thus, the solution is:
Therefore, the sum of the two sides is:
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A parallelogram has a base of 
. The perimeter of the parallelogram is 
. Find the sum of the two adjacent sides to the base.
A parallelogram has a base of
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A parallelogram must have two sets of congruent/parallel opposite sides. This parallelogram must have two sides with a measurement of 
and two base sides each with a length of 
. In this question, you are provided with the information that the parallelogram has a base of 
and a total perimeter of 
. Thus, work backwards using the perimeter formula in order to find the sum of the two adjacent sides to the base.
, where and are the measurements of adjacent sides.
Thus, the solution is:
A parallelogram must have two sets of congruent/parallel opposite sides. This parallelogram must have two sides with a measurement of
Thus, the solution is:
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