GRE Math : How to find the area of a parallelogram

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Example Question #11 : How To Find The Area Of A Parallelogram

A parallelogram has a base of $180\textup{mm}^{2}$ and a height measurement that is $\frac{1}{3}$ the base length. Find the area of the parallelogram.

Possible Answers:

$504\textup{mm}^{2}$

$540\textup{mm}^{2}$

$5\textup{,}400\textup{mm}^{2}$

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

$10\textup{,800}\textup{mm}^{2}$

Correct answer:

$10\textup{,800}\textup{mm}^{2}$

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:

$area=base\times height$
Before applying the formula you must find $\frac{1}{3}$ of $180=\frac{180}{3}=60$ .

The solution is:

$area=180\times 60=10,800$

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

$18\times6=108$

There were two total zeros in the factors, so tack on two zeros to the product:
10,800

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Example Question #12 : How To Find The Area Of A Parallelogram

Grerectangle

ABCD is a rectangle.

Quantity A: The area of AEB

Quantity B: The area BEC

Possible Answers:

The two quantities are equal.

Quantity B is greater.

Quantity A is greater.

The relationship cannot be determined.

Correct answer:

The two quantities are equal.

Explanation:

The area of a triangle is $\frac{1}{2}bh;b:base,h:height$

Consider the rectangle ABCD
Grerectangle

As a rectangle:

$\overline{AB}=\overline{DC}$

$\overline{AD}=\overline{BC}$

With appearing directly in the center of the rectangle.

The area of $AEB=\frac{1}{2}(\overline{AB})(\frac{1}{2}\overline{BC})=\frac{1}{4}(\overline{AB})(\overline{BC})$

Notice that the $\frac{1}{2}\overline{BC}$ term corresponds to the triangle's height.

The area of $BEC=\frac{1}{2}(\overline{BC})(\frac{1}{2}\overline{AB})=\frac{1}{4}(\overline{BC})(\overline{AB})$

The two quantities are equal.

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Example Question #11 : Quadrilaterals

Parallelogram gre

Using the parallelogram shown above, find the area.

Possible Answers:

$6480\textup{ in}^{2}$

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

$504\textup{ ft}^{2}$

$540\textup{ ft}^{2}$

Not enough information is provided.

Correct answer:

$6480\textup{ in}^{2}$

Explanation:

This problem provides both the base and height measurements, thus apply the formula:

$area=base\times height$

$area=9\times 5=45$ $ft^{2}$

To find an equivalent answer in inches, you must convert the measurements to inches FIRST, and then multiply:

$9\times12=108$

$5\times12=60$

Therefore, our area in square inches is:

$108\times60=6480\ \textup{inches}$

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GRE Math : How to find the area of a parallelogram

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #11 : How To Find The Area Of A Parallelogram

Example Question #12 : How To Find The Area Of A Parallelogram

Example Question #11 : Quadrilaterals

All GRE Math Resources

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