To solve the problem of finding the perimeter of each shape, we need to sum the lengths of all the sides of each shape. Let's go through each shape step by step.
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Shape 1: Square
- All sides are equal, and each side is given as \(6 \, \text{cm}\).
- Perimeter of a square = \(4 \times \text{side length}\).
- Perimeter = \(4 \times 6 = 24 \, \text{cm}\).
Answer for Shape 1: \(24 \, \text{cm}\)
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Shape 2: Rectangle
- The dimensions are given as \(6 \, \text{m}\) (length) and \(1 \, \text{m}\) (width).
- Perimeter of a rectangle = \(2 \times (\text{length} + \text{width})\).
- Perimeter = \(2 \times (6 + 1) = 2 \times 7 = 14 \, \text{m}\).
Answer for Shape 2: \(14 \, \text{m}\)
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Shape 3: Trapezoid
- The sides are given as \(7 \, \text{cm}\), \(7 \, \text{cm}\), \(4 \, \text{cm}\), and \(10 \, \text{cm}\).
- Perimeter = sum of all sides.
- Perimeter = \(7 + 7 + 4 + 10 = 28 \, \text{cm}\).
Answer for Shape 3: \(28 \, \text{cm}\)
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Shape 4: Irregular Polygon
- The sides are given as \(8 \, \text{cm}\), \(7 \, \text{cm}\), \(3 \, \text{cm}\), \(4 \, \text{cm}\), \(4 \, \text{cm}\), and \(12 \, \text{cm}\).
- Perimeter = sum of all sides.
- Perimeter = \(8 + 7 + 3 + 4 + 4 + 12 = 38 \, \text{cm}\).
Answer for Shape 4: \(38 \, \text{cm}\)
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Shape 5: Composite Rectangle
- The shape consists of two rectangles joined together.
- The outer dimensions are \(12 \, \text{cm}\) (length) and \(8 \, \text{cm}\) (height).
- The smaller rectangle inside has dimensions \(4 \, \text{cm}\) (width) and \(3 \, \text{cm}\) (height).
- To find the perimeter, we sum the outer edges:
- Top edge: \(12 \, \text{cm}\)
- Bottom edge: \(12 \, \text{cm}\)
- Left edge: \(8 \, \text{cm}\)
- Right edge: \(8 \, \text{cm}\)
- Inner vertical edge: \(4 \, \text{cm}\)
- Inner horizontal edge: \(3 \, \text{cm}\)
- Perimeter = \(12 + 12 + 8 + 8 + 4 + 3 = 47 \, \text{cm}\).
Answer for Shape 5: \(47 \, \text{cm}\)
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Shape 6: Irregular Polygon with Cutouts
- The shape is a large rectangle with smaller rectangular cutouts.
- The large rectangle has dimensions \(10 \, \text{cm}\) (length) and \(5 \, \text{cm}\) (height).
- There are four smaller rectangles cut out, each with dimensions \(2 \, \text{cm}\) (length) and \(2 \, \text{cm}\) (height).
- To find the perimeter, we consider only the outer edges of the large rectangle because the cutouts do not affect the outer perimeter.
- Perimeter of the large rectangle = \(2 \times (\text{length} + \text{width})\).
- Perimeter = \(2 \times (10 + 5) = 2 \times 15 = 30 \, \text{cm}\).
Answer for Shape 6: \(30 \, \text{cm}\)
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Final Answers:
1. \(24 \, \text{cm}\)
2. \(14 \, \text{m}\)
3. \(28 \, \text{cm}\)
4. \(38 \, \text{cm}\)
5. \(47 \, \text{cm}\)
6. \(30 \, \text{cm}\)
\[
\boxed{24, 14, 28, 38, 47, 30}
\]
Parent Tip: Review the logic above to help your child master the concept of math perimeter worksheet.
