# Intermediate Geometry : Parallelograms

## Example Questions

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### Example Question #1 : Parallelograms

The length of a parallelogram is  cm and the width is  cm. One of its diagonals measures  cm. Find the length of the other diagonal.

Explanation:

The formula for the relationship between diagonals and sides of a parallologram is

,

where  represents one diagonal,

represents the other diagonal,

represents a side, and

So, in this problem, substitute the known values and solve for the missing diagonal.

So, the missing diagonal is  cm.

### Example Question #2 : Parallelograms

In the parallogram above, find the length of the labeled diagonal.

Explanation:

In a parallogram, diagonals bisect one another, thus you can set the two segments that are labeled in the picture equal to one another, then solve for .

So,

.

If , then you can substitute 14 into each labeled segment, to get a total of 52.

### Example Question #3 : Parallelograms

In the parallogram below, find the length of the labeled diagonal.

Explanation:

In a parallelogram, the diagonals bisect one another, so you can set the labeled segments equal to each other and then solve for .

.

If , then you substitute 6 into each labeled segment, to get a total of 40.

### Example Question #4 : Parallelograms

In the parallelogram above, find the length of the labeled diagonal.

Explanation:

In a parallelogram, the diagonals bisect each other, so you can set the labeled segments equal to one another and then solve for

.

Then, substitute 4.8 for  in each labeled segment to get a total of 11.2 for the diagonal length.

### Example Question #5 : Parallelograms

Suppose a square has an area of 6.  What is the diagonal of the parallelogram?

Explanation:

Write the formula to find the side of the square given the area.

Find the side.

The diagonal of the square can be solved by using the Pythagorean Theorem.

Substitute and solve for the diagonal, .

### Example Question #6 : Parallelograms

If the side length of a square is , what is the diagonal of the square?

Explanation:

Write the diagonal formula for a square.

Substitute the side length and reduce.

### Example Question #7 : Parallelograms

Parallelogram  has diagonals  and  and .

True, false, or undetermined: Parallelogram  is a rectangle.

True

Undetermined

False

False

Explanation:

One characteristic of a rectangle is that its diagonals are congruent. Since the diagonals of Parallelogram  are of different lengths, it cannot be a rectangle.

### Example Question #8 : Parallelograms

Parallelogram  has diagonals  and  and .

True, false, or undetermined: Parallelogram  is a rhombus.

False

Undetermined

True

Undetermined

Explanation:

One characteristic of a rhombus is that its diagonals are perpendicular; no restrictions exist as to their lengths. Whether or not the diagonals are perpendicular is not stated, so the figure may or may not be a rhombus.

### Example Question #9 : Parallelograms

Find the perimeter of the parallelogram shown above.

Explanation:

In order to find the perimeter of this parallelogram, apply the formula:
.

The solution is:

### Example Question #10 : Parallelograms

Find the perimeter of the parallelogram shown above.

Explanation:

To find the perimeter of this parallelogram, first find the length of the side: .

Since, , the side must be .

Then apply the formula:

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