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

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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

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

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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