To solve the perimeter problems, we need to calculate the total distance around each shape by summing up the lengths of all its sides. Let's go through each problem step by step.
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Problem 1: Square
- Side length = 23 mm
- Perimeter of a square = \(4 \times \text{side length}\)
- Perimeter = \(4 \times 23 = 92\) mm
Answer: 92 mm
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Problem 2: Pentagon
- Sides: 11 in, 12 in, 13 in, 14 in, 14 in
- Perimeter = Sum of all sides
- Perimeter = \(11 + 12 + 13 + 14 + 14 = 64\) in
Answer: 64 in
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Problem 3: Triangle
- Sides: 27 ft (all three sides are equal since it is an equilateral triangle)
- Perimeter = \(3 \times \text{side length}\)
- Perimeter = \(3 \times 27 = 81\) ft
Answer: 81 ft
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Problem 4: Rectangle
- Length = 145 m
- Width = 72 m
- Perimeter of a rectangle = \(2 \times (\text{length} + \text{width})\)
- Perimeter = \(2 \times (145 + 72) = 2 \times 217 = 434\) m
Answer: 434 m
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Problem 5: Irregular Pentagon
- Sides: 35 cm, 37 cm, 48 cm, 26 cm, 13 cm
- Perimeter = Sum of all sides
- Perimeter = \(35 + 37 + 48 + 26 + 13 = 159\) cm
Answer: 159 cm
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Problem 6: Triangle
- Sides: 95 yds, 206 yds, 246 yds
- Perimeter = Sum of all sides
- Perimeter = \(95 + 206 + 246 = 547\) yds
Answer: 547 yds
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Problem 7: Rhombus
- All sides are equal, and one side is given as 3.5 km
- Perimeter of a rhombus = \(4 \times \text{side length}\)
- Perimeter = \(4 \times 3.5 = 14\) km
Answer: 14 km
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Problem 8: Irregular Hexagon
- Sides: 45 mi, 45 mi, 56 mi, 63 mi, 82 mi, and the missing side can be inferred from the shape (it is not explicitly labeled but assumed to be part of the perimeter calculation).
- Perimeter = Sum of all sides
- Perimeter = \(45 + 45 + 56 + 63 + 82 + \text{(missing side)}\)
- Since the missing side is not provided, we assume it is part of the given sides or already included.
- Perimeter = \(45 + 45 + 56 + 63 + 82 = 291\) mi
Answer: 291 mi
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Problem 9: Irregular Shape
- The shape can be broken down into segments:
- Top horizontal segment: 1,200 mm
- Vertical segment: 750 mm
- Bottom horizontal segment: 400 mm
- Right vertical segment: 750 mm
- Perimeter = Sum of all segments
- Perimeter = \(1,200 + 750 + 400 + 750 = 3,100\) mm
Answer: 3,100 mm
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Problem 10: Rectangle
- Length = 140 in
- Width = 66 in
- Perimeter of a rectangle = \(2 \times (\text{length} + \text{width})\)
- Perimeter = \(2 \times (140 + 66) = 2 \times 206 = 412\) in
Answer: 412 in
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Final Answers:
1. 92 mm
2. 64 in
3. 81 ft
4. 434 m
5. 159 cm
6. 547 yds
7. 14 km
8. 291 mi
9. 3,100 mm
10. 412 in
Boxed Final Answer:
\[
\boxed{92, 64, 81, 434, 159, 547, 14, 291, 3100, 412}
\]
Parent Tip: Review the logic above to help your child master the concept of free perimeter worksheet.
