Calculate the perimeter of a parallelogram with sides 6 3/4 inches and 5 1/2 inches?

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Calculate the perimeter of a parallelogram with sides 6 3/4 inches and 5 1/2 inches?

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Answer 1 · 2015-12-25T15:14:22

$24 \frac{1}{2}$ $24 1/2$ $in$ $"in"$

Explanation:

Parallelograms have opposite and congruent sides.

This means that the $4$ $4$ sides of the parallelogram are

$6 \frac{3}{4}, 6 \frac{3}{4}, 5 \frac{1}{2}, 5 \frac{1}{2}$ $6 3/4,6 3/4, 5 1/2, 5 1/2$

To find the perimeter, add these all together.

First convert the mixed fractions into improper fractions.

$6 \frac{3}{4} = \frac{27}{4}$ $6 3/4=27/4$

$5 \frac{1}{2} = \frac{11}{2}$ $5 1/2=11/2$

Now, when we add these, we should have a common denominator between

$\frac{27}{4}$ $27/4$ and $\frac{11}{2}$ $11/2$

$\frac{11}{2} = \frac{22}{4}$ $11/2=22/4$

Now, add the $4$ $4$ sides:

$\frac{27}{4} + \frac{27}{4} + \frac{22}{4} + \frac{22}{4} = \frac{98}{4}$ $27/4+27/4+22/4+22/4=98/4$

$\Rightarrow \frac{49}{2} = 24 \frac{1}{2}$ $=>49/2=24 1/2$ $in$ $"in"$

Answer 2 · 2016-05-02T08:25:13

This one is an exercise in fractions which can be done mentally, rather than by the pure application of a method. The fact that the perimeter is asked for is citing the reason to add fractions.

Explanation:

P = $6 \frac{3}{4} + 5 \frac{1}{2} + 6 \frac{3}{4} + 5 \frac{1}{2}$ $6 3/4 + 5 1/2 + 6 3/4 + 5 1/2$

Work with the whole numbers first, giving: 6+5+6+5 = 22

Now add the fractions: $\frac{1}{2} + \frac{1}{2} = 1$ $1/2 + 1/2 = 1$ and $\frac{3}{4} + \frac{3}{4} = 1 \frac{1}{2}$ $3/4 +3/4 = 1 1/2$

So, the perimeter = $22 + 1 + 1 \frac{1}{2} = 24 \frac{1}{2}$ $22 + 1 + 1 1/2 = 24 1/2$

But, let's look at $\frac{3}{4} + \frac{3}{4} = 1 \frac{1}{2}$ $3/4 +3/4 = 1 1/2$ again.

$\frac{3}{4} = \frac{1}{2} + \frac{1}{4}$ $3/4 = 1/2 + color(red)(1/4)$

In $\frac{3}{4} + \frac{3}{4}$ $3/4 + 3/4$ we have $\frac{1}{2} + \frac{1}{4} + \frac{3}{4}$ $1/2 + color(red)(1/4) + color(red)(3/4)$

The two fractions in red add to make 1, then the $\frac{1}{2}$ $1/2$ can be added giving $1 \frac{1}{2}$ $1 1/2$

Try to work questions like this in your head first, then you can check on paper, or as a last resort, with a calculator.

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Calculate the perimeter of a parallelogram with sides 6 3/4 inches and 5 1/2 inches?

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