How to find the perimeter of a polygon - High School Math

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Question

All segments of the polygon meet at right angles (90 degrees). The length of segment $\overline{AB}$ is 10. The length of segment $\overline{BC}$ is 8. The length of segment $\overline{DE}$ is 3. The length of segment $\overline{GH}$ is 2.

Find the perimeter of the polygon.

Answer

The perimeter of the polygon is 46. Think of this polygon as a rectangle with two of its corners "flipped" inwards. This "flipping" changes the area of the rectangle, but not its perimeter; therefore, the top and bottom sides of the original rectangle would be 12 units long $\dpi{100} \small (10+2=12)$ . The left and right sides would be 11 units long $\dpi{100} \small (8+3=11)$ . Adding all four sides, we find that the perimeter of the recangle (and therefore, of this polygon) is 46.

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Question

What is the perimeter of a regular nonagon with a side length of ?

Answer

To find the perimeter of a regular polygon, we take the length of each side, , and multiply it by the number of sides, .

In a nonagon the number of sides is , and in this example the side length is .

The perimeter is .

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Question

What is the perimeter of a regular hendecagon with a side length of 32?

Answer

To find the perimeter of a regular hendecagon you must first know the number of sides in a hendecagon is 11.

When you know the number of sides of a regular polygon to find the perimeter you must multiply the side length by the number of sides.

In this case it is .

The answer for the perimeter is .

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Question

Find the perimeter of the following octagon:

Answer

The formula for the perimeter of an octagon is .

Plugging in our values, we get:

$P = 8(12\ m)$

$P = 96\ m$

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