### All Intermediate Geometry Resources

## Example Questions

### Example Question #1 : How To Find The Length Of The Side Of A Parallelogram

Find the perimeter of the following box in inches:

**Possible Answers:**

**Correct answer:**

The answer is .

You can find the perimeter by adding all of its respective sides as such:

.

Adding like terms will result in

If you chose , you multiplied the two sides to find the area.

If you chose , you only added two sides. Perimeter involves all 4 sides; so double the width and length.

Just remember, the width is 12 added to . Not 12 times the side of .

### Example Question #1 : How To Find The Length Of The Side Of A Parallelogram

A parallelogram has an area of . If the height is , what is the length of the base?

**Possible Answers:**

Cannot be determined

**Correct answer:**

If the area of a parallelogram is given as with a height of , we can refer back to the equation for the area of a parallelogram:

, where is height and is the length of the base.

This very quickly becomes a problem of substituting in values and finding the value of an unknown variable, in this case, :

### Example Question #3 : How To Find The Length Of The Side Of A Parallelogram

A parallelogram has a base of and an area of . What is the height of the parallelogram?

**Possible Answers:**

**Correct answer:**

In order to find the height of this parallelogram apply the formula:

### Example Question #4 : How To Find The Length Of The Side Of A Parallelogram

A parallelogram has a height of and an area of . What is the length of the base of the parallelogram?

**Possible Answers:**

**Correct answer:**

To find the missing side of this parallelgram apply the formula:

Thus, the solution is:

### Example Question #5 : How To Find The Length Of The Side Of A Parallelogram

Given that a parallelogram has a height of and an area of . Find the base of the parallelogram.

**Possible Answers:**

**Correct answer:**

In order to find the base of this parallelogram apply the formula:

Thus, the solution is:

### Example Question #6 : How To Find The Length Of The Side Of A Parallelogram

Given: Quadrilateral with diagonal ; .

True or false: From the information given, it follows that Quadrilateral is a parallelogram.

**Possible Answers:**

True

False

**Correct answer:**

True

Corresponding parts of congruent triangles are, by definition, congruent. Thus, from the statement , it follows that:

and

Quadrilateral therefore has two sets of congruent opposite sides. This is a sufficient condition for the quadrilateral to be a parallelogram.

### Example Question #1 : How To Find The Length Of The Side Of A Parallelogram

Quadrilateral is both a rhombus and a rectangle.

True or false: Quadrilateral must be a square.

**Possible Answers:**

False

True

**Correct answer:**

True

A rhombus is defined to be a parallelogram with four congruent sides; a rectangle is defined to be a parallelogram with four right angles.

A square is defined to be a parallelogram with four congruent sides *and* four right angles. If a parallelogram is both a rhombus and a rectangle, then it fits both characteristics and is therefore a square.

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