Parallelograms - GRE Quantitative Reasoning
Card 0 of 232
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
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:
Compare your answer with the correct one above
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?
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
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?
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:
Compare your answer with the correct one above
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?
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.
Compare your answer with the correct one above
Figure is a parallelogram.
What is in the figure above?
Figure
What is
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?
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:
Compare your answer with the correct one above
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?
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.
Compare your answer with the correct one above
Figure is a parallelogram.
What is in the figure above?
Figure
What is
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
Compare your answer with the correct one above
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?
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:
Compare your answer with the correct one above
A parallelogram has a base of 
and a height of 
. Find the area of the parallelogram.
A parallelogram has a base of
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:
Compare your answer with the correct one above
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
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:
Compare your answer with the correct one above
Using the parallelogram shown above, find the area.
Using the parallelogram shown above, find the area.
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:
Compare your answer with the correct one above
A parallelogram has a base of 
and a height of 
. Find the area of the parallelogram.
A parallelogram has a base of
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:
Compare your answer with the correct one above
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
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:
Compare your answer with the correct one above
Using the parallelogram shown above, find the area.
Using the parallelogram shown above, find the area.
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:
Compare your answer with the correct one above
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
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:
Compare your answer with the correct one above
A parallelogram has a base of 
and a height of 
. Find the area of the parallelogram.
A parallelogram has a base of
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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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.
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:
Compare your answer with the correct one above
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
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:
Compare your answer with the correct one above