### All ACT Math Resources

## Example Questions

### Example Question #1 : Pentagons

The perimeter of a regular pentagon is . What is the length of one side?

**Possible Answers:**

**Correct answer:**

A problem like this is very easy. A regular pentagon just looks like:

All of its sides are equal. Therefore, you know that , where is the length of one side. Solving for , you get .

### Example Question #2 : How To Find The Length Of The Side Of A Pentagon

If the perimeter of a given regular pentagon is . What is the length of one side of this regular pentagon in inches?

**Possible Answers:**

**Correct answer:**

Use the formula for perimeter to solve for the side length of the regular pentagon:

Where is the perimeter and is the length of a side.

In this case:

### Example Question #21 : Plane Geometry

Find the length of each side for regular pentagon with a perimeter of .

**Possible Answers:**

**Correct answer:**

Use the formula for perimeter to solve for the side length:

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

Find the length of one side for a regular pentagon with a perimeter of .

**Possible Answers:**

**Correct answer:**

Use the formula for perimeter to solve for the side length:

### Example Question #2 : How To Find The Length Of The Side Of A Pentagon

Find the length of each side for a regular pentagon with a perimeter of .

**Possible Answers:**

**Correct answer:**

Use the formula for perimeter to solve for the side length:

### Example Question #21 : Plane Geometry

If the side of a pentagon is , what is the diagonal of the pentagon?

**Possible Answers:**

**Correct answer:**

Write the formula for finding the diagonal of a pentagon.

Plug in the side length and simplify.

### Example Question #1 : Pentagons

Find the length of the diagonal for a pentagon with a a side length of .

**Possible Answers:**

**Correct answer:**

Use the formula for the diagonal of a pentagon:

### Example Question #27 : Geometry

Find the length of the diagonal for a pentagon with a perimeter of .

**Possible Answers:**

**Correct answer:**

1. Use the formula for perimeter to solve for the side length:

2. Use the formula for the diagonal of a pentagon:

### Example Question #21 : Geometry

Find the diagonal for a pentagon with a perimeter of .

**Possible Answers:**

**Correct answer:**

1. Use the formula for perimeter to solve for the side length:

2. Use the formula for the diagonal of a pentagon:

### Example Question #21 : Plane Geometry

If a side of the pentagon is , what is the diagonal of the pentagon?

**Possible Answers:**

**Correct answer:**

Write the diagonal formula for a pentagon.

Substitute the side length and find the diagonal.

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