# Intermediate Geometry : How to find the length of the side of a parallelogram

## Example Questions

### Example Question #31 : Parallelograms

Find the perimeter of the following box in inches:       Explanation:

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 #32 : Parallelograms

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

Cannot be determined     Explanation:

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 #33 : Parallelograms

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

In order to find the height of this parallelogram apply the formula:   ### Example Question #34 : Parallelograms

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

To find the missing side of this parallelgram apply the formula: Thus, the solution is:  ### Example Question #1 : 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.     Explanation:

In order to find the base of this parallelogram apply the formula: Thus, the solution is:   ### Example Question #2 : 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.

True

False

True

Explanation:

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 #3 : 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.

True

False 