ISEE Lower Level Math : How to find the perimeter of a parallelogram

Study concepts, example questions & explanations for ISEE Lower Level Math

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Example Questions

Example Question #1 : Quadrilaterals

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What is the perimeter of parallelogram ABCD?

Possible Answers:

\(\displaystyle 8\)

\(\displaystyle 7.5\)

Cannot be determined

\(\displaystyle 15\)

\(\displaystyle 16\)

Correct answer:

\(\displaystyle 16\)

Explanation:

The perimeter of a parallelogram is very easy to find. You just need to add up all the sides. However, you need to notice that the sides "across" from each other are equal on parallelograms. So, your figure could be redrawn:

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The perimeter of your figure is therefore:

\(\displaystyle Perimeter = 5+5+3+3=16\)

Example Question #1 : How To Find The Perimeter Of A Parallelogram

A parallelogram has a side length of \(\displaystyle 3 in\).  It also has a side length of \(\displaystyle 5 in\).  Calculate the perimeter. 

Possible Answers:

\(\displaystyle 16 in\)

\(\displaystyle 10 in\)

\(\displaystyle 9 in\)

\(\displaystyle 8 in\)

\(\displaystyle 15 in\)

Correct answer:

\(\displaystyle 16 in\)

Explanation:

A parallelogram has four sides and its opposite sides are equal in length.  Therefore, if it has one side length of\(\displaystyle 3 in\), it also has another side length of of \(\displaystyle 3 in\).  Since we know one of its side lenghts is \(\displaystyle 5 in\), then the remaining side is \(\displaystyle 5in\).  We can add all 4 side lengths \(\displaystyle \left ( 3 in, 3 in, 5 in, 5in\right )\)to calculate the perimeter. 

Example Question #3 : Quadrilaterals

What is the perimeter of a parallelogram if the base is \(\displaystyle 8\), the other side is \(\displaystyle 2\), and the height is \(\displaystyle 3\)?

Possible Answers:

\(\displaystyle 16\)

\(\displaystyle 10\)

\(\displaystyle 22\)

\(\displaystyle 24\)

\(\displaystyle 20\)

Correct answer:

\(\displaystyle 20\)

Explanation:

The perimeter of a parallelogram is the sum of all four sides or the sum of two times each side length.  The side lengths are \(\displaystyle 2\) and \(\displaystyle 8\) so the perimeter is \(\displaystyle (2*8)+(2*2)=20\).

Example Question #1 : Plane Geometry

Find the perimeter of the given parallelogram:

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Possible Answers:

\(\displaystyle 384 mi\)

\(\displaystyle 160 mi\)

\(\displaystyle 320 mi\)

\(\displaystyle 192 mi\)

Correct answer:

\(\displaystyle 320 mi\)

Explanation:

Find the perimeter of the given parallelogram:

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The perimeter of any shape can be found by adding up the lentghs of its sides.

In this case, we have four sides. 2 that are 16 miles long, and 2 that are 144 miles long.

Find perimeter as follows:

\(\displaystyle P=2(16)+2(144)=32+288=320\)

Making our answer 320 miles

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