### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #5 : Parallelograms

The area of the Parallelogram is . Give its perimeter in terms of .

**Possible Answers:**

**Correct answer:**

The height of the parallelogram is , and the base is . By the 45-45-90 Theorem, . Since the product of the height and the base of a parallelogram is its area,

Also by the 45-45-90 Theorem,

, and

The perimeter of the parallelogram is

### Example Question #6 : Parallelograms

Calculate the perimeter of the above parallelogram if .

**Possible Answers:**

**Correct answer:**

By the 45-45-90 Theorem,

The perimeter of the parallelogram is

### Example Question #7 : Parallelograms

Calculate the perimeter of the above parallelogram if .

**Possible Answers:**

**Correct answer:**

By the 30-60-90 Theorem:

, and

The perimeter of the parallelogram is

### Example Question #8 : Parallelograms

Find the perimeter of a parallelogram with a base of 6in and a side of length 8in.

**Possible Answers:**

**Correct answer:**

A parallelogram has 4 sides. A base (where the opposite side is equal) and a side (where the opposite side is equal). So, we will use the following formula:

where *b* is the base and *s* is the side of the parallelogram.

We know the base has a length of 6in. We also know the side has a length of 8in.

Knowing this, we can substitute into the formula. We get