# SAT II Math II : Perimeter

## Example Questions

### Example Question #1 : Perimeter

Refer to the above figure. Quadrilateral  is a square. What is the perimeter of Polygon ?

Explanation:

is both one side of Square  and the hypotenuse of ;  its hypotenuse can be calculated from the lengths of the legs using the Pythagorean Theorem:

.

Since Square  has four congruent sides, each side has length 13.

The perimeter of Polygon  is

### Example Question #2 : Perimeter

Note:  Figure NOT drawn to scale

Refer to the above figure, which shows a rectangular garden (in green) surrounded by a dirt path (in orange) seven feet wide throughout. What is the perimeter of the garden?

Explanation:

The inner rectangle, which represents the garden, has length and width  feet and  feet, respectively, so its perimeter is

feet.

### Example Question #27 : Geometry

Refer to the above figure, which shows a square garden (in green) surrounded by a dirt path (in orange). The dirt path is seven feet wide throughout. Which of the following polynomials gives the perimeter of the garden in feet?

Explanation:

The sidelength of the garden, in feet, is  feet less than that of the entire lot, or

;

The perimeter, in feet, of the garden is four times this:

### Example Question #3 : Perimeter

You have a pentagonal-shaped lot with side lengths of 120ft ,30ft, 55ft, 60ft, and a longest side which is triple the length of the third longest side. What is the perimeter around the lot?

Explanation:

You have a pentagonal-shaped lot with side lengths of 120ft,30ft, 55ft, 60 ft, and a longest side which is triple the length of the third longest side. What is the perimeter around the lot?

So, we have a five-sided lot and are given 4 sides, and the means to find the 5th.

The longest side is triple the length of the third longest side:

The third longest side is 60 feet, therefore, the longest side is 180 ft

Find the perimeter by adding up all the sides:

So our answer is 445 feet

### Example Question #3 : Perimeter

Find the circumference of a circle with diameter of 15.

Explanation:

The circumference of a circle is denoted by the formula  where r is the radius of the circle. The problem gives us the diameter of the circle which must be used to find the radius.

Plug the radius into the formula for the area of a circle

### Example Question #30 : Geometry

If the sides of a triangle are , , and , what is the perimeter?

Explanation:

The perimeter of a triangle is the sum of all three sides of the triangle.

Add all the side lengths.

Expand the terms in the bracket and remove all parentheses.

Combine like-terms.

### Example Question #5 : Perimeter

If the side length of a rectangle is 6 inches, what is the perimeter?

Explanation:

A square can be a rectangle, but a rectangle cannot be a square.   We cannot assume that the width is known given just the length of the rectangle.  There is not enough information to determine the perimeter just by the side length alone.

### Example Question #6 : Perimeter

The image represents a track is a regular hexagon with perimeter one half of a mile.

Selena starts at Point A and runs clockwise to Point D. She then runs directly from  Point D to Point A. How far does she run?

Explanation:

The perimeter of the hexagonal track is one half of a mile. One mile is equal to 5,280 feet, so one half of a mile is equal to

Each of the six congruent sides measures one sixth of this, or

The hexagonal track is recreated below, with its six radii constructed - the center is called .

The radii divide the hexagon into six equilateral triangles, so each of the radii has length equal to one side of the hexagon. Selena's path takes her along , and  - a path equivalent in distance to five sides of the hexagon. Therefore, Selena runs a distance of

### Example Question #4 : Perimeter

What is the perimeter of a square if the area is  units squared?

Explanation:

Determine the length of the square by using the given area.

Substitute the area.

There are four congruent sides in a square, which means the perimeter is four times the side.

### Example Question #7 : Perimeter

What is the perimeter of a right triangle with a base of 6, and a height of 8?

Explanation:

Use the Pythagorean Theorem to determine the hypotenuse.

Substitute the base and height.

Square root both sides to find the hypotenuse.

Add the sides to determine the perimeter.