How to find the perimeter of a parallelogram - 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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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:

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

Compare your answer with the correct one above

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:

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

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

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

Compare your answer with the correct one above

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:

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

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

Compare your answer with the correct one above

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

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

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

Compare your answer with the correct one above

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:

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

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

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

Compare your answer with the correct one above

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:

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

Compare your answer with the correct one above

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:

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

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

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

Compare your answer with the correct one above

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:

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

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

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

Compare your answer with the correct one above

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:

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

Compare your answer with the correct one above

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:

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

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

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

Compare your answer with the correct one above

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