Math Problem Statement

Work out the perimeter of the shape below.

Solution

Let's solve this problem by determining the perimeter of the given composite shape. The perimeter is the sum of all the outer sides of the shape.

Dimensions from the image:

  1. The vertical side on the left: 8cm8 \, \text{cm}
  2. The top horizontal side: 4cm4 \, \text{cm}
  3. The vertical side at the top-right: 2cm2 \, \text{cm}
  4. The middle horizontal side: 6cm6 \, \text{cm}
  5. The small vertical side at the bottom-right: 3cm3 \, \text{cm}
  6. The bottom horizontal side: 4cm4 \, \text{cm}

Step-by-step calculation:

  • Add the vertical sides: 8cm+2cm+3cm=13cm.8 \, \text{cm} + 2 \, \text{cm} + 3 \, \text{cm} = 13 \, \text{cm}.

  • Add the horizontal sides: 4cm+6cm+4cm=14cm.4 \, \text{cm} + 6 \, \text{cm} + 4 \, \text{cm} = 14 \, \text{cm}.

  • Total perimeter: 13cm+14cm=27cm.13 \, \text{cm} + 14 \, \text{cm} = 27 \, \text{cm}.

Final Answer:

The perimeter of the shape is 27 cm.

Would you like further clarification or help with another part of the problem?


Here are five related questions for practice:

  1. How do you find the perimeter of a rectangle with given length and width?
  2. What is the difference between area and perimeter of a shape?
  3. How can you determine missing side lengths of composite shapes?
  4. Can the perimeter of a shape ever be less than its largest side? Why or why not?
  5. How would you calculate the perimeter of a circle?

Tip: Always double-check that you include all sides when calculating the perimeter of composite shapes!

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Math Problem Analysis

Mathematical Concepts

Geometry
Perimeter
Composite Shapes

Formulas

Perimeter = Sum of all outer sides

Theorems

No specific theorems; involves additive properties of lengths

Suitable Grade Level

Grades 6-8