Parallelograms - GRE Quantitative Reasoning
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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
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
Compare your answer with the correct one above
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
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.
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
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:
Compare your answer with the correct one above
A parallelogram has a base measurement of 
. The perimeter of the parallelogram is 
. Find the measurement of an adjacent side to the base.
A parallelogram has a base measurement of
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 length of one missing side that is adjacent 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:
Compare your answer with the correct one above
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
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 given 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:
Compare your answer with the correct one above
A parallelogram has a base of 
. An adjacent side to the base has a length of 
. Find the perimeter of the parallelogram.
A parallelogram has a base of
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 
. To find the perimeter of the parallelogram apply the formula:
, where and are the measurements of adjacent sides.
Thus, the solution is:
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:
Compare your answer with the correct one above
A parallelogram has a base measurement of 
. The perimeter of the parallelogram is 
. Find the measurement for an adjacent side to the base.
A parallelogram has a base measurement of
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 
. However, to solve this problem you must first convert the provided perimeter measurement from feet to inches. Since an inch is 
of 
foot, 
feet is equal to
inches.
Now, you can work backwards using the formula:
, where and are the measurements of adjacent sides.
Thus, the solution is:
A parallelogram must have two sets of congruent/parallel opposite sides. Therefore, this parallelogram must have two sides with a measurement of
Now, you can work backwards using the formula:
Thus, the solution is:
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Using the parallelogram shown above, find the length of side 
Using the parallelogram shown above, find the length of side
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:
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:
Compare your answer with the correct one above
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
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:
Compare your answer with the correct one above
A parallelogram has a base of 
. An adjacent side to the base has a length of 
. Find the perimeter of the parallelogram.
A parallelogram has a base of
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 
To find the perimeter of the parallelogram apply the formula:
, where and are the measurements of adjacent sides.
Thus, the solution is:
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:
Compare your answer with the correct one above
A parallelogram has a base of 
. The perimeter of the parallelogram is 
. Find the length for an adjacent side to the base.
A parallelogram has a base of
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 
. To solve for the missing side, work backwards using the perimeter formula:
, where and are the measurements of adjacent sides.
Thus, the solution is:
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:
Compare your answer with the correct one above
A quadrilateral has equal sides, each with a length of 
.
Quantity A: The area of the quadrilateral.
Quantity B: The perimeter of the quadrilateral.
A quadrilateral has equal sides, each with a length of
Quantity A: The area of the quadrilateral.
Quantity B: The perimeter of the quadrilateral.
We are told that the shape is a quadrilateral and that the sides are equal; beyond that, we do not know what specific kind of kind of quadrilateral it is, outside of the fact that it is a rhombus. The perimeter, the sum of the sides, is 
.
If this shape were a square, the area would also be 
; however, if the interior angles were not all equivalent, the area would be smaller than this.
The relationship cannot be determined.
We are told that the shape is a quadrilateral and that the sides are equal; beyond that, we do not know what specific kind of kind of quadrilateral it is, outside of the fact that it is a rhombus. The perimeter, the sum of the sides, is
If this shape were a square, the area would also be
The relationship cannot be determined.
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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
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
Compare your answer with the correct one above
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
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:
Compare your answer with the correct one above
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.
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:
Compare your answer with the correct one above
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
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:
Compare your answer with the correct one above
A parallelogram has a base measurement of . The perimeter of the parallelogram is . Find the measurement of an adjacent side to the base.
A parallelogram has a base measurement of
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 length of one missing side that is adjacent 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:
Compare your answer with the correct one above
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
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 given 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:
Compare your answer with the correct one above
A parallelogram has a base of . An adjacent side to the base has a length of . Find the perimeter of the parallelogram.
A parallelogram has a base of
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 . To find the perimeter of the parallelogram apply the formula:
, where and are the measurements of adjacent sides.
Thus, the solution is:
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:
Compare your answer with the correct one above