# GED Math : Perimeter and Sides

## Example Questions

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### Example Question #1 : Perimeter And Sides

Identify the above polygon.

Pentagon

Octagon

Hexagon

Octagon

Explanation:

A polygon with eight sides is called an octagon.

### Example Question #2 : Perimeter And Sides

Refer to the above figure.

Which of the following is not a valid alternative name for Polygon ?

Polygon

Polygon

Polygon

Polygon

Polygon

Explanation:

In naming a polygon, the vertices must be written in the order in which they are positioned, going either clockwise or counterclockwise. Of the four choices, only Polygon  violates this convention, since  and  are not adjacent vertices (nor are  and ).

### Example Question #1 : Perimeter And Sides

Refer to the above figure. All angles shown are right angles.

What is the perimeter of the figure?

Explanation:

The figure can be viewed as the composite of rectangles. As such, we can take advantage of the fact that opposite sides of a rectangle have the same length, as follows:

Now that the missing sidelengths are known, we can add the sidelengths to find the perimeter:

### Example Question #2 : Perimeter And Sides

Refer to the above figure.

Which of the following segments is a diagonal of Pentagon  ?

Explanation:

A diagonal of a polygon is a segment whose endpoints are nonconsecutive vertices of the polygon. Of the four choices, only  fits this description.

### Example Question #5 : Perimeter And Sides

Classify the above polygon.

Octagon

Hexagon

Rhombus

Pentagon

Octagon

Explanation:

A polygon with eight sides is called an octagon.

### Example Question #6 : Perimeter And Sides

Classify the above polygon.

Trapezoid

Octagon

Hexagon

Pentagon

Hexagon

Explanation:

A polygon with six sides is called a hexagon.

### Example Question #3 : Perimeter And Sides

Hexagon  is regular. If diagonals  and  are constructed, which of the following classifications applies to Quadrilateral ?

I) Rectangle

II) Rhombus

III) Square

IV) Trapezoid

II only

I, II, and III only

I only

IV only

I only

Explanation:

The figure described is below.

Since the hexagon is regular, its sides are congruent, and its angles each have measure .

Also, each of the triangles are isosceles, and their acute angles measure  each. This means that each of the four angles of Quadrilateral  measures , so Quadrilateral  is a rectangle. However, not all sides are congruent, so it is not a rhombus. Also, since it is a rectangle, it cannot be a trapezoid.

The correct response is I only.

### Example Question #4 : Perimeter And Sides

The above figure is a regular octagon. Give its perimeter in yards.

Explanation:

A regular octagon has eight sides of equal length, so multiply the length of one side by eight:

feet.

Divide by three to get the equivalent in yards:

yards.

### Example Question #5 : Perimeter And Sides

What is the perimeter of a semicircle with an area of ?

Explanation:

Write the formula for the area of a semicircle.

Substitute the area.

Multiply by 2, and divide by pi on both sides.

The equation becomes:

Square root both sides and factor the right side.

The diameter is double the radius.

The circumference is half the circumference of a full circle.

The perimeter is the sum of the diameter and the half circumference.

### Example Question #10 : Perimeter And Sides

A hexagon has a perimeter of 90in.  Find the length of one side.

Explanation:

A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is:

where a is the length of any side. Now, to find the length of one side, we will solve for a

We know the perimeter of the hexagon is 90in. So, we will substitute and solve for a. We get

Therefore, the length of one side of the hexagon is 15in.

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