To solve the problem of finding the perimeter of each symmetric shape using the given information, we need to carefully analyze each shape and use the provided measurements. Let's go through each shape step by step.
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Shape 1: Regular Pentagon
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Given Information: One side length is 5 units.
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Symmetry: The pentagon is regular, meaning all sides are equal.
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Perimeter Calculation:
- A regular pentagon has 5 equal sides.
- Perimeter = \( 5 \times \text{side length} \)
- Perimeter = \( 5 \times 5 = 25 \) units.
Answer for Shape 1: \( \boxed{25} \)
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Shape 2: Regular Hexagon
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Given Information: One side length is 4 units.
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Symmetry: The hexagon is regular, meaning all sides are equal.
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Perimeter Calculation:
- A regular hexagon has 6 equal sides.
- Perimeter = \( 6 \times \text{side length} \)
- Perimeter = \( 6 \times 4 = 24 \) units.
Answer for Shape 2: \( \boxed{24} \)
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Shape 3: Square
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Given Information: One side length is 7 units.
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Symmetry: The square is regular, meaning all sides are equal.
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Perimeter Calculation:
- A square has 4 equal sides.
- Perimeter = \( 4 \times \text{side length} \)
- Perimeter = \( 4 \times 7 = 28 \) units.
Answer for Shape 3: \( \boxed{28} \)
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Shape 4: Equilateral Triangle
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Given Information: One side length is 6 units.
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Symmetry: The triangle is equilateral, meaning all sides are equal.
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Perimeter Calculation:
- An equilateral triangle has 3 equal sides.
- Perimeter = \( 3 \times \text{side length} \)
- Perimeter = \( 3 \times 6 = 18 \) units.
Answer for Shape 4: \( \boxed{18} \)
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Shape 5: Regular Octagon
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Given Information: One side length is 3 units.
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Symmetry: The octagon is regular, meaning all sides are equal.
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Perimeter Calculation:
- A regular octagon has 8 equal sides.
- Perimeter = \( 8 \times \text{side length} \)
- Perimeter = \( 8 \times 3 = 24 \) units.
Answer for Shape 5: \( \boxed{24} \)
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Shape 6: Regular Star (Pentagram)
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Given Information: Each outer segment of the star is 2 units.
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Symmetry: The star is regular, meaning all outer segments are equal.
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Perimeter Calculation:
- A regular pentagram has 10 equal outer segments (5 points, each with 2 segments).
- Perimeter = \( 10 \times \text{segment length} \)
- Perimeter = \( 10 \times 2 = 20 \) units.
Answer for Shape 6: \( \boxed{20} \)
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Final Answers
1. \( \boxed{25} \)
2. \( \boxed{24} \)
3. \( \boxed{28} \)
4. \( \boxed{18} \)
5. \( \boxed{24} \)
6. \( \boxed{20} \)
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Explanation
For each shape, we used the property of symmetry to determine that all sides or segments were equal. Then, we multiplied the number of sides or segments by the given length to find the perimeter. This approach ensures accuracy and consistency in solving problems involving symmetric shapes.
Parent Tip: Review the logic above to help your child master the concept of lines of symmetry worksheet.
