# High School Math : Other Polygons

## Example Questions

### Example Question #1 : How To Find The Area Of A Polygon

Find the area of the shaded region:

Explanation:

The formula for the area of the shaded region is

where  is the radius of the circle.

Plugging in our values, we get:

### Example Question #2 : How To Find The Area Of A Polygon

Find the area of the following octagon:

Explanation:

The formula for the area of a regular octagon is:

Plugging in our values, we get:

### Example Question #3 : How To Find The Area Of A Polygon

Find the area of a rectangle with a base of  and a width of  in terms of .

Explanation:

This problem simply becomes a matter of FOILing (first outer inner last)

The area of the shape is Base times Height.

So, multiplying  and   using FOIL, we get an area of

### Example Question #4 : How To Find The Area Of A Polygon

Find the area of a square whose diagonal is .

Explanation:

If the diagonal of a square is , we can use the pythagorean theorem to solve for the length of the sides.

= length of side of the square

Doing so, we get

To find the area of the square, we square , resulting in .

### Example Question #1 : How To Find An Angle In A Polygon

What is the magnitude of the interior angle of a regular nonagon?

Explanation:

The equation to calculate the magnitude of an interior angle is , where  is equal to the number of sides.

For our question, .

### Example Question #2 : How To Find An Angle In A Polygon

What is the interior angle measure of any regular heptagon?

Explanation:

To find the angle of any regular polygon you find the number of sides, . In this example, .

You then subtract 2 from the number of sides yielding 5.

Take 5 and multiply it by 180 degrees to yield the total number of degrees in the regular heptagon.

Then to find one individual angle we divide 900 by the total number of angles, 7.

### Example Question #3 : How To Find An Angle In A Polygon

A regular polygon with  sides has exterior angles that measure  each. How many sides does the polygon have?

This figure cannot exist.

Explanation:

The sum of the exterior angles of any polygon, one per vertex, is . As each angle measures , just divide 360 by 1.5 to get the number of angles.

### Example Question #4 : How To Find An Angle In A Polygon

What is the interior angle measure of any regular nonagon?

Explanation:

To find the angle of any regular polygon you find the number of sides , which in this example is .

You then subtract  from the number of sides yielding .

Take  and multiply it by  degrees to yield a total number of degrees in the regular nonagon.

Then to find one individual angle we divide  by the total number of angles .

### Example Question #5 : How To Find An Angle In A Polygon

What is the measure of one exterior angle of a regular seventeen-sided polygon (nearest tenth of a degree)?

Explanation:

The sum of the measures of the exterior angles of any polygon, one per vertex, is . In a regular polygon, all of these angles are congruent, so divide 360 by 17 to get the measure of one exterior angle:

### Example Question #6 : How To Find An Angle In A Polygon

What is the measure of one exterior angle of a regular twenty-three-sided polygon (nearest tenth of a degree)?