To solve the problem of finding the perimeters of the given regular shapes, we need to use the formula for the perimeter of a regular polygon:
\[
\text{Perimeter} = \text{Number of sides} \times \text{Length of one side}
\]
Let's go through each shape step by step:
---
1. Square
-
Shape: Square
-
Side length: 6 cm
-
Number of sides: 4
\[
\text{Perimeter} = 4 \times 6 \, \text{cm} = 24 \, \text{cm}
\]
---
2. Equilateral Triangle
-
Shape: Equilateral triangle
-
Side length: 4 in
-
Number of sides: 3
\[
\text{Perimeter} = 3 \times 4 \, \text{in} = 12 \, \text{in}
\]
---
3. Regular Pentagon
-
Shape: Regular pentagon
-
Side length: 5 cm
-
Number of sides: 5
\[
\text{Perimeter} = 5 \times 5 \, \text{cm} = 25 \, \text{cm}
\]
---
4. Regular Octagon
-
Shape: Regular octagon
-
Side length: 3 m
-
Number of sides: 8
\[
\text{Perimeter} = 8 \times 3 \, \text{m} = 24 \, \text{m}
\]
---
5. Regular Octagon
-
Shape: Regular octagon
-
Side length: 8 mm
-
Number of sides: 8
\[
\text{Perimeter} = 8 \times 8 \, \text{mm} = 64 \, \text{mm}
\]
---
6. Regular Hexagon
-
Shape: Regular hexagon
-
Side length: 7 in
-
Number of sides: 6
\[
\text{Perimeter} = 6 \times 7 \, \text{in} = 42 \, \text{in}
\]
---
Final Answers
1. Perimeter of the square: \( \boxed{24 \, \text{cm}} \)
2. Perimeter of the equilateral triangle: \( \boxed{12 \, \text{in}} \)
3. Perimeter of the regular pentagon: \( \boxed{25 \, \text{cm}} \)
4. Perimeter of the regular octagon: \( \boxed{24 \, \text{m}} \)
5. Perimeter of the regular octagon: \( \boxed{64 \, \text{mm}} \)
6. Perimeter of the regular hexagon: \( \boxed{42 \, \text{in}} \)
---
Explanation
The perimeter of a regular polygon is calculated by multiplying the number of sides by the length of one side. This formula works because all sides of a regular polygon are equal in length. By identifying the number of sides and the side length for each shape, we can easily compute the perimeter.
Final Answer Boxed:
\[
\boxed{24 \, \text{cm}, 12 \, \text{in}, 25 \, \text{cm}, 24 \, \text{m}, 64 \, \text{mm}, 42 \, \text{in}}
\]
Parent Tip: Review the logic above to help your child master the concept of perimeter of a polygon worksheet.
