How to find the area of a parallelogram - GRE Quantitative Reasoning

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Question

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.

Answer

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:

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Question

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.

Answer

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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Question

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

Answer

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 $\frac{1}{5}$ of $20=\frac{20}{5}=4$ .

The final solution is:

$area=20\times 4=80$

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Question

Using the parallelogram shown above, find the area.

Answer

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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Question

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

Answer

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:

$area=15\times 8=120$

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Question

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

Answer

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:

$area=base\times height$
Before applying the formula you must find $\frac{1}{2}$ of $18=\frac{18}{2}=9$ .

The solution is:

$area=18\times 9=162$

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Question

Using the parallelogram shown above, find the area.

Answer

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:

$area=98\times44=4,312$

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Question

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.

Answer

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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Question

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

Answer

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 , as well as $6\frac{2}{4}$ to . 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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Question

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

Answer

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:

$area=10\times 5=50$

$4\times2=8$

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Question

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

Answer

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:

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Question

Find the area for the parallelogram shown above.

Answer

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:

$area=15\times 19=285$

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Question

ABCD is a rectangle.

Quantity A: The area of AEB

Quantity B: The area BEC

Answer

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

Consider the rectangle ABCD

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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Question

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.

Answer

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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Question

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

Answer

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 $\frac{1}{5}$ of $20=\frac{20}{5}=4$ .

The final solution is:

$area=20\times 4=80$

Compare your answer with the correct one above

Question

Using the parallelogram shown above, find the area.

Answer

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:

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

Compare your answer with the correct one above

Question

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

Answer

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:

$area=15\times 8=120$

Compare your answer with the correct one above

Question

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

Answer

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:

$area=base\times height$
Before applying the formula you must find $\frac{1}{2}$ of $18=\frac{18}{2}=9$ .

The solution is:

$area=18\times 9=162$

Compare your answer with the correct one above

Question

Using the parallelogram shown above, find the area.

Answer

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:

$area=98\times44=4,312$

Compare your answer with the correct one above

Question

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.

Answer

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:

$area=12\times 3=36$

Compare your answer with the correct one above

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