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## Example Questions

### Example Question #1 : Dsq: Calculating The Perimeter Of A Polygon

Given a regular hexagon and a regular octagon, which, if either, has the greater perimeter?

Statement 1: The sidelength of the octagon is one foot.

Statement 2: The sidelength of the hexagon is fifteen inches.

**Possible Answers:**

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

**Correct answer:**

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Each of the two statements allows you to find out the perimeter of one of the polygons by multiplying its sidelength by the number of its sides. However, neither statement offers any clues to the perimeter of the other polygon. Both statements together, however, allow you to determine and to compare both perimeters.

### Example Question #132 : Geometry

You are given a regular hexagon and a regular pentagon. Which one has the greater perimeter?

Statement 1: The hexagon and the pentagon have the same area

Statement 2: The apothem of the hexagon is greater than that of the pentagon

**Possible Answers:**

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

**Correct answer:**

The area of a polygon is one-half the product of its perimeter and its apothem (the perpendicular distance from the center to a side). Therefore,

,

or

Therefore, the perimeter can be determined from both area and apothem, but not from one alone. Neither statement alone gives you enough information, but from both statements together, it can be determined that the pentagon has the greater perimeter.

### Example Question #2 : Polygons

Note: Figure NOT drawn to scale. All angles shown are right angles.

What is the perimeter of the above figure?

Statement 1:

Statement 2:

**Possible Answers:**

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

**Correct answer:**

The figure can be seen as a rectangle cut out of an rectangle.

The perimeter of the composite figure is

.

However, since opposite sides of a rectangle are congruent, then, as can be seen in the figure, and .

The perimeter can then be rewritten:

Therefore, it is necessary and sufficient to know and ; the other four sidelengths are not needed to determine the perimeter of the figure.

### Example Question #3 : Polygons

Consider regular decagon .

I) Side is 56 inches long.

II) Side plus Side is equivalent to 112 inches.

Find the perimeter of .

**Possible Answers:**

Neither statement is sufficient to answer the question. More information is needed.

Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.

Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.

Both statements are needed to answer the question.

Either statement is sufficient to answer the question.

**Correct answer:**

Either statement is sufficient to answer the question.

To find perimeter, we need the length of all the sides. Note that we are dealing with a regular polygon, so all of its sides are equal.

Statement I gives us one side length. Multiply the side by ten (decagons have ten sides):

Statement II gives us the length of two sides together. Multiply by 5 to get the total perimeter:

### Example Question #135 : Geometry

Consider pentagon .

I) Side has the same length as side *,* 5 inches.

II) Side is one-third the length of side , and sides and have the same length as side .

What is the perimeter of ?

**Possible Answers:**

Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.

Either statement is sufficient to answer the question.

Both statements are needed to answer the question.

**Correct answer:**

Both statements are needed to answer the question.

Consider pentagon .

I) Side has the same length as side *,* 5 inches.

II) Side is one-third the length of sides , and .

What is the perimeter of ?

To find perimeter, we need to know the length of all the sides.

Statement I gives us the lengths of two sides.

Statement II relates one of the sides given in Statement I to the other three sides:

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