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
- The side length is given as \(6 \, \text{cm}\).
- A square has 4 equal sides.
- Perimeter = \(4 \times \text{side length}\)
- 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).
- A rectangle has 2 lengths and 2 widths.
- Perimeter = \(2 \times (\text{length} + \text{width})\)
- 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 \(8 \, \text{cm}\), \(7 \, \text{cm}\), \(4 \, \text{cm}\), \(4 \, \text{cm}\), \(3 \, \text{cm}\), and \(12 \, \text{cm}\).
- Perimeter = Sum of all sides
- Perimeter = \(8 + 7 + 4 + 4 + 3 + 12 = 38 \, \text{cm}\)
Answer for Shape 4: \(38 \, \text{cm}\)
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Shape 5: Composite Rectangle
- The shape consists of a large rectangle with a smaller rectangle cut out from one corner.
- The outer dimensions of the large rectangle are \(12 \, \text{cm}\) (length) and \(8 \, \text{cm}\) (width).
- The smaller rectangle that is cut out has dimensions \(4 \, \text{cm}\) (length) and \(3 \, \text{cm}\) (width).
- To find the perimeter, we consider only the outer edges of the shape.
- Perimeter = Sum of all outer edges
- Perimeter = \(12 + 8 + 8 + (12 - 4) + 3 + (4 - 3) = 12 + 8 + 8 + 8 + 3 + 1 = 40 \, \text{cm}\)
Answer for Shape 5: \(40 \, \text{cm}\)
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Shape 6: Irregular Polygon
- The shape is a rectangle with smaller rectangles cut out from each corner.
- The outer dimensions of the large rectangle are \(10 \, \text{cm}\) (length) and \(5 \, \text{cm}\) (width).
- Each corner cut-out is a small square with side length \(2 \, \text{cm}\).
- To find the perimeter, we consider only the outer edges of the shape.
- Perimeter = Sum of all outer edges
- Perimeter = \(10 + 5 + 10 + 5 = 30 \, \text{cm}\) (since the cuts do not affect the outer perimeter)
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. \(40 \, \text{cm}\)
6. \(30 \, \text{cm}\)
\[
\boxed{24, 14, 28, 38, 40, 30}
\]
Parent Tip: Review the logic above to help your child master the concept of math worksheet perimeter.
