GRE Math : Parallelograms

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Example Questions

Example Question #1311 : Gre Quantitative Reasoning

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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:

$area=base\times height$ $\displaystyle area=base\times height$

The solution is:

$area=7.5\times5=37.5$ $\displaystyle area=7.5\times5=37.5$

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Example Question #1 : Parallelograms

A parallelogram has a base of $\displaystyle 20$ and a height measurement that is $\frac{1}{5}$ $\displaystyle \frac{1}{5}$ the base length. Find the area of the parallelogram.

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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Example Question #2 : Parallelograms

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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Example Question #3 : Parallelograms

A parallelogram has a base of $\displaystyle 18$ and a height measurement that is $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ the base length. Find the area of the parallelogram.

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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Example Question #4 : Parallelograms

Parallelogram gre

Using the parallelogram shown above, find the area.

Possible Answers:

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

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

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

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

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

Correct answer:

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

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:

$area=base\times height$ $\displaystyle area=base\times height$

The solution is:

$area=98\times44=4,312$ $\displaystyle area=98\times44=4,312$

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Example Question #1 : Quadrilaterals

A parallelogram has a base of $\displaystyle 12$ meters and a height measurement that is $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ the base length. Find the area of the parallelogram.

Possible Answers:

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

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

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

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

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

Correct answer:

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

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:

$area=base\times height$ $\displaystyle area=base\times height$
Before applying the formula you must find $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ of $\displaystyle 12$.

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

The solution is:

$area=12\times 3=36$ $\displaystyle area=12\times 3=36$

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Example Question #2 : Quadrilaterals

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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:

$area=base\times height$ $\displaystyle area=base\times height$

The solution is:

$area=8.5\times 6.5=55.25$ $\displaystyle area=8.5\times 6.5=55.25$

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

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

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

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

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Example Question #1 : Parallelograms

Parallelogram gre

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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Example Question #1 : Quadrilaterals

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

Possible Answers:

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

$4\textup{,}900$ $\displaystyle 4\textup{,}900$

Not enough information is provided.

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

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

Correct answer:

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

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:

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

The solution is:

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

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

$14\times7=98$ $\displaystyle 14\times7=98$

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

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Example Question #1 : Parallelograms

Parallelogram gre

Find the area for the parallelogram shown above.

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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GRE Math : Parallelograms

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1311 : Gre Quantitative Reasoning

Example Question #1 : Parallelograms

Example Question #2 : Parallelograms

Example Question #3 : Parallelograms

Example Question #4 : Parallelograms

Example Question #1 : Quadrilaterals

Example Question #2 : Quadrilaterals

Example Question #1 : Parallelograms

Example Question #1 : Quadrilaterals

Example Question #1 : Parallelograms

All GRE Math Resources

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