GRE Math : Quadrilaterals

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Example Questions

Example Question #1 : Quadrilaterals

A parallelogram has a base of $7\tfrac{1}{2}\textup{ inches}$ and a height of $5\textup{ inches}$ . Find the area of the parallelogram.

Possible Answers:

$9\textup{ inches}^{2}$

$18.75\textup{ inches}^{2}$

$37.5\textup{ inches}^{2}$

$35.25\textup{ inches}^{2}$

$40.5\textup{ inches}^{2}$

Correct answer:

$37.5\textup{ inches}^{2}$

Explanation:

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:

$area=base\times height$

The solution is:

$area=7.5\times5=37.5$

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Example Question #122 : Geometry

A parallelogram has a base of and a height measurement that is $\frac{1}{5}$ the base length. Find the area of the parallelogram.

Possible Answers:

$160\textup{ units}^{2}$

$80\textup{ units}^{2}$

$40\textup{ units}^{2}$

$20\textup{ units}^{2}$

$55\textup{ units}^{2}$

Correct answer:

$80\textup{ units}^{2}$

Explanation:

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Example Question #123 : Geometry

A parallelogram has a base of $15\textup{m}$ and a height of $8\textup{m}$ . Find the area of the parallelogram.

Possible Answers:

$60\textup{m}^{2}$

$130\textup{m}^{2}$

$30\textup{m}^{2}$

$120\textup{m}^{2}$

$120\textup{cm}^{2}$

Correct answer:

$120\textup{m}^{2}$

Explanation:

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Example Question #124 : Geometry

A parallelogram has a base of and a height measurement that is $\frac{1}{2}$ the base length. Find the area of the parallelogram.

Possible Answers:

$81\textup{ units}^{2}$

$172\textup{ units}^{2}$

$150\textup{ units}^{2}$

$162\textup{ units}^{2}$

$88\textup{ units}^{2}$

Correct answer:

$162\textup{ units}^{2}$

Explanation:

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Example Question #125 : Geometry

Parallelogram gre

Using the parallelogram shown above, find the area.

Possible Answers:

$4\textup{,}312\textup{mm}^{2}$

$980\textup{mm}^{2}$

$3\textup{,}256\textup{mm}^{2}$

$3\textup{,}156\textup{mm}^{2}$

$988\textup{mm}^{2}$

Correct answer:

$4\textup{,}312\textup{mm}^{2}$

Explanation:

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Example Question #2 : Quadrilaterals

A parallelogram has a base of meters and a height measurement that is $\frac{1}{4}$ the base length. Find the area of the parallelogram.

Possible Answers:

$18\textup{m}^{2}$

$36\textup{m}^{2}$

$27\textup{m}^{2}$

$48\textup{m}^{2}$

$52\textup{m}^{2}$

Correct answer:

$36\textup{m}^{2}$

Explanation:

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:

$area=base\times height$
Before applying the formula you must find $\frac{1}{4}$ of .

$\frac{1}{4}\times12=\frac{12}{4}=12\div4=3$

The solution is:

$area=12\times 3=36$

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Example Question #3 : Quadrilaterals

A parallelogram has a base of $8\frac{1}{2}$ and a height of $6\frac{2}{4}$ . Find the area of the parallelogram.

Possible Answers:

$52.25\textup{ units}^{2}$

$60\textup{ units}^{2}$

$54\textup{ units}^{2}$

$55.5\textup{ units}^{2}$

$55.25\textup{ units}^{2}$

Correct answer:

$55.25\textup{ units}^{2}$

Explanation:

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:

$area=base\times height$

The solution is:

$area=8.5\times 6.5=55.25$

Note: prior to applying the formula, the answer choices require you to be able to convert $8\frac{1}{2}$ to 8.5 , as well as $6\frac{2}{4}$ to 6.5 . Or, you could have converted the mixed numbers to improper fractions and then multiplied the two terms:

$8\frac{1}{2}=\frac{17}{2}$

$6\frac{2}{4}=\frac{26}{4}=\frac{13}{2}$

$\frac{17}{2}\times \frac{13}{2}=\frac{221}{4}=55.25$

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Example Question #1 : Quadrilaterals

Parallelogram gre

Find the area of the parallelogram shown above, excluding the interior space occupied by the blue rectangle.

Possible Answers:

$42\textup{ units}^{2}$

$24\textup{ units}^{2}$

$38\textup{ units}^{2}$

$58\textup{ units}^{2}$

$50\textup{ units}^{2}$

Correct answer:

$42\textup{ units}^{2}$

Explanation:

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:

$area=base\times height$

Additionally, this problem requires you to find the area of the interior rectangle. This can be simply found by applying the formula: $area=length\times width$

Thus, the solution is:

$area=10\times 5=50$

$4\times2=8$

50-8=42

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Example Question #1 : Quadrilaterals

A parallelogram has a base of 140 and a height measurement that is $\frac{1}{2}$ the base length. Find the area of the parallelogram.

Possible Answers:

$9\textup{,}800\textup{ units}^{2}$

$4\textup{,}900$

$8\textup{,}200\textup{ units}^{2}$

$1\textup{,}800\textup{ units}^{2}$

Not enough information is provided.

Correct answer:

$9\textup{,}800\textup{ units}^{2}$

Explanation:

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:

$area=base\times height$
Before applying the formula you must find $\frac{1}{2}$ of $140=\frac{140}{2}=70$ .

The solution is:

$area=140\times 70=9,800$

Note: when working with multiples of ten remove zeros and then tack back onto the product.

$14\times7=98$

There were two total zeros in the factors, so tack on two zeros to the product:
9,800

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Example Question #2 : Quadrilaterals

Parallelogram gre

Find the area for the parallelogram shown above.

Possible Answers:

$307\textup{ units}^{2}$

$157.5\textup{ units}^{2}$

$142.5\textup{ units}^{2}$

$285\textup{ units}^{2}$

$305\textup{ units}^{2}$

Correct answer:

$285\textup{ units}^{2}$

Explanation:

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GRE Math : Quadrilaterals

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : Quadrilaterals

Example Question #122 : Geometry

Example Question #123 : Geometry

Example Question #124 : Geometry

Example Question #125 : Geometry

Example Question #2 : Quadrilaterals

Example Question #3 : Quadrilaterals

Example Question #1 : Quadrilaterals

Example Question #1 : Quadrilaterals

Example Question #2 : Quadrilaterals

All GRE Math Resources

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