### All HiSET: Math Resources

## Example Questions

### Example Question #11 : Properties Of Polygons And Circles

A five sided irregular polygon has sides of the following lengths:

Find its perimeter.

**Possible Answers:**

**Correct answer:**

Perimeters can be calculated using the following formula.

In this formula, the variable, , represents a side of the polygon.

Substitute and solve.

### Example Question #12 : Properties Of Polygons And Circles

The area of a square is . In terms of , give the perimeter of the square.

**Possible Answers:**

**Correct answer:**

The length of one side of a square is equal to the square root of its area, so, if the area of a square is , the common sidelength is . Since a square comprises four sides of equal length, the perimeter is equal to four times this length, or .

### Example Question #2 : Perimeter And Circumference

The perimeter of a regular octagon is . Give the length of one side.

**Possible Answers:**

**Correct answer:**

A regular octagon has eight sides of equal length. Its perimeter is equal to the sum of the lengths of its sides, so the length of one side can be computed by dividing the perimeter by 8, as follows:

,

the correct response.

### Example Question #1 : Perimeter And Circumference

Give the perimeter of a regular octagon in yards if the length of each side is feet.

**Possible Answers:**

yards

yards

yards

yards

yards

**Correct answer:**

yards

The perimeter of a regular octagon - the sum of the lengths of its (eight congruent) sides - is eight times the common sidelength, so the perimeter of the octagon is feet. One yard is equivalent to three feet, so divide this by conversion factor 3 to get yards - the correct response.

### Example Question #1 : Perimeter And Circumference

Hexagon is regular. Give the perimeter of Trapezoid .

**Possible Answers:**

**Correct answer:**

A regular hexagon can be divided into six equilateral triangles, as follows:

The perimeter of Trapezoid can be seen to be .