How to find the perimeter of a parallelogram - Intermediate Geometry

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Question

Find the perimeter (in inches) of a parallelogram that has a base of $\small \small 1\frac{3}{4} ft$ and a side length of $\small 1\frac{1}{2} ft$ .

Answer

To find the perimeter of the parallelogram apply the formula: $\small Perimeter=2(base+side)$ . However, to find the solution with the correct unit, convert $\small 1\frac{3}{4} feet=21 inches$ and $\small 1\frac{1}{2}feet=18 inches$ . We can convert feet into inches because .

Thus, the solution is:

$\small P=2(21+18)$
$\small P=2(39)$
$\small P=78$

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Question

A parallelogram has a base length of $\small 15$ and a side length of $\small \frac{base}{2}$ . Find the perimeter of the parallelogram.

Answer

To solve this problem, apply the formula: $\small P=2(base+side)$ .

Since, the side length is equal to $\small \frac{base}{2}$ , the solution is:

$\small P=2(15+\frac{15}{2})$

$\small P=2(15+7.5)$

$\small P=2(22.5)=45$

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Question

Find the perimeter of the parallelogram shown above.

Answer

In order to find the perimeter of this parallelogram, apply the formula:
$\small Perimeter=2(base+side)$ .

The solution is:

$\small P=2(8+5)$

$\small \small P=2(13)=26$

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Question

If a parallelogram has a base that is three times the length of the side, and the side length is equal to $\small \frac{3}{4}foot$ , what is the perimeter of the parallelogram in inches?

Answer

The side length of this parallelogram is $\small \frac{3}{4}$ foot, which is equivalent to $\small 9$ inches because $12in=1ft \rightarrow \frac{3}{4}\cdot 12=\frac{36}{4}=9in$ .

Thus, the base must be $\small 9\times 3=27$ .

Then, apply the formula $\small p=2(base+side)$

$\small P=2(27+9)$

$\small P=2(36)=72$

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Question

Find the perimeter of the parallelogram shown above.

Answer

To find the perimeter of this parallelogram, first find the length of the side: $\small h\times\frac{1}{3}$ .

Since, $\small h=48$ , the side must be $\small 48\div 3=16$ .

Then apply the formula:

$\small p=2(base+side)$

$\small p=2(96+16)$

$\small p=2(112)=224$

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Question

A parallelogram has a side length $\small \frac{1}{4}$ that of the length of the base. If the length of the base is $\small \small 524mm$ , find the perimeter of the parallelogram.

Answer

Since the side is $\small \frac{1}{4}$ the length of the base, the side is equal to $\small 524\div4=131$ .

Then apply the formula $\small p=2(base+side)$ .

The solution is:

$\small p=2(524+131)$
$\small p=2(655)=1,310$

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Question

If a parallelogram has a base of $\small 9$ and a side length of $\small \frac{9}{3}$ , find the perimeter of the parallelogram.

Answer

To solve this problem, apply the formula: $\small p=2(base+side)$ .

Thus, the solution is:

$\small p=2\left(9+\frac{9}{3}\right)$

$\small p=2(9+3)$

$\small p=2(12)=24$

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Question

Find the perimeter of the parallelogram shown above.

Answer

To solve this problem, apply the formula $\small \small perimeter=2(base+side)$ .

Since the length of the side is not provided in the figure, apply the formula $\small a^2 +b^2=c^2$ , where $\small a=h$ , $\small b=2$ and $\small c=$ the side of the parallelogram.

The solution is:

$\small 6^2+2^2=c^2$
$\small 36+4=c^2$
$\small 40=c^2$
$\small c=\sqrt{40}$

Thus,

$\small p=2(9+\sqrt{40})$

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Question

A parallelogram has a base that is $\small 5$ times greater than the length of the side of the parallelogram. If the length of the side is $\small \small \sqrt{169}$ , what is the perimeter of the parallelogram?

Answer

To solve this problem, first find the $\small \sqrt{169}=13$ . Then to find the length of the base: $\small 13\times 5=65$

Then apply the formula:

$\small p=2(base+side)$ .

$\small p=2(65+13)$

$\small \small p=2(78)=156$

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