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, as 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, 248 yds
- Perimeter = Sum of all sides
- Perimeter = \(95 + 206 + 248 = 549\) yds
Answer: 549 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 last side can be inferred from the shape (it is not explicitly labeled but can be assumed to be part of the perimeter)
- Perimeter = Sum of all sides
- Perimeter = \(45 + 45 + 56 + 63 + 82 + \text{(last side)}\)
- Since the last side is not labeled, we assume it is part of the given sides or can be calculated if needed. However, based on the provided sides:
- Perimeter = \(45 + 45 + 56 + 63 + 82 = 291\) mi
Answer: 291 mi
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Problem 9: Irregular Shape
- The shape is a combination of straight lines.
- Sides: 1,200 mm, 400 mm, 780 mm, and two vertical sides of 660 mm each (inferred from the shape).
- Perimeter = Sum of all sides
- Perimeter = \(1,200 + 400 + 780 + 660 + 660 = 3,700\) mm
Answer: 3,700 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. 549 yds
7. 14 km
8. 291 mi
9. 3,700 mm
10. 412 in
Boxed Final Answer:
\[
\boxed{92, 64, 81, 434, 159, 549, 14, 291, 3700, 412}
\]
Parent Tip: Review the logic above to help your child master the concept of perimeter worksheets.
