Question

polygons
example find the perimeter.
find the perimeter of a regular polygon by multiplying
the length of a side by the number of sides.
find the perimeter of an irregular polygon by adding
the lengths of all sides.
perimeter ( = 8+7+5+12+10+9 = 51 mathrm{~cm} )
directions calculate the perimeters.

1. regular nonagon with a side of 9 in.

2.

1. regular heptagon with a side of 5 in.

4.

1. regular pentagon with a side of 15 in.

6.

1. regular hexagon with a side of 11 in.

8.

1. regular triangle with a side of 24 in.

10.

Explanation:

Step1: Calculate perimeter of regular nonagon

A nonagon has 9 sides. Given side length \(a = 9\) in. Perimeter \(P=9\times a\).
\(P = 9\times9=81\) in.

Step2: Calculate perimeter of irregular pentagon (problem 2)

Add all side lengths: \(10 + 6+7 + 8+9\).
\(10+6 = 16\), \(16+7=23\), \(23 + 8=31\), \(31+9 = 40\) ft.

Step3: Calculate perimeter of regular heptagon

A heptagon has 7 sides. Given side length \(a = 5\) in. Perimeter \(P=7\times a\).
\(P=7\times5 = 35\) in.

Step4: Calculate perimeter of irregular hexagon (problem 4)

Add all side lengths: \(8+12 + 9+13+11+15\).
\(8+12=20\), \(20+9 = 29\), \(29+13=42\), \(42+11 = 53\), \(53+15=68\) cm.

Step5: Calculate perimeter of regular pentagon

A pentagon has 5 sides. Given side length \(a = 15\) in. Perimeter \(P=5\times a\).
\(P=5\times15=75\) in.

Step6: Calculate perimeter of irregular pentagon (problem 6)

Add all side lengths: \(5+6+12+13\).
\(5+6 = 11\), \(11+12=23\), \(23+13 = 36\) ft.

Step7: Calculate perimeter of regular hexagon

A hexagon has 6 sides. Given side length \(a = 11\) in. Perimeter \(P=6\times a\).
\(P=6\times11 = 66\) in.

Step8: Calculate perimeter of irregular heptagon (problem 8)

Add all side lengths: \(6+13+12+14+10+9+9\).
\(6+13=19\), \(19+12=31\), \(31+14=45\), \(45+10=55\), \(55+9=64\), \(64+9=73\) cm.

Step9: Calculate perimeter of regular triangle

A triangle has 3 sides. Given side length \(a = 24\) in. Perimeter \(P=3\times a\).
\(P=3\times24=72\) in.

Step10: Calculate perimeter of irregular octagon (problem 10)

Add all side lengths: \(10+11+16+18+9+12+8+7\).
\(10+11=21\), \(21+16=37\), \(37+18=55\), \(55+9=64\), \(64+12=76\), \(76+8=84\), \(84+7=91\) ft.

Answer:

1. \(81\) in.
2. \(40\) ft.
3. \(35\) in.
4. \(68\) cm.
5. \(75\) in.
6. \(36\) ft.
7. \(66\) in.
8. \(73\) cm.
9. \(72\) in.
10. \(91\) ft.