How to find the perimeter of a parallelogram - Math

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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$ .

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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.

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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.

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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?

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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.

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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.

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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.

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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.

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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?

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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

Note: Figure NOT drawn to scale.

$a = 18; \textrm{in} ,b=26; \textrm{in},h=12; \textrm{in}$ , where and represent side lengths of the parallelogram and represents the height.

Find the perimeter of the parallelogram in the diagram.

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Answer

The perimeter of the parallelogram is the sum of the four side lengths - here, that formula becomes

.

Note that the height is irrelevant to the answer.

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Question

Find the perimeter of the parallelogram.

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Answer

To find the perimeter of a parallelogram, add the lengths of the sides. Opposite sides of a parallelogram are equivalent.

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Question

If the perimter of a parallelogram is and one of the sides is , what is the other side length?

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Answer

The perimeter of a parallelogram is found by adding up all four sides.

Since there are two pairs of side with equal lengths, two sides must have a length of .

So the perimeter would be

or .

To find the value of the other side length, you would divide the remaining perimeter not include in the other sides by .

So $20\div2=10$ .

That means the other side length would be .

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Question

If a parallelogram has side lengths of and , what is the perimeter?

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Answer

The perimeter of a parallelogram is two times the two side lengths and add them together.

$\P=s_1+s_2+s_3+s_4 \s_1=s_3 \s_2=s_4 \P=s_a+s_a+s_b+s_b \P=2s_a+2s_b$

Therefore, this particular problem becomes as follows.

and

so

.

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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$ .

Tap to reveal answer

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.

Tap to reveal answer

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.

Tap to reveal answer

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?

Tap to reveal answer

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.

Tap to reveal answer

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.

Tap to reveal answer

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.

Tap to reveal answer

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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