Math Problem Statement

find the perimeter

Find the perimeter of the given L-shaped figure with dimensions provided in the image.

Solution

To find the perimeter of the given shape, we need to add up the lengths of all the sides.

Let's break down the shape:

  • The bottom horizontal length is 6 cm.
  • The vertical length on the right side is 3 cm.
  • The horizontal length on the top right is 4 cm (since the total bottom length is 6 cm, and the vertical length on the left is 2 cm, which implies the remaining top length is 62=46 - 2 = 4 cm).
  • The vertical length on the left side is 2 cm.
  • The horizontal length on the top left is 2 cm.
  • The vertical length on the left side going up is 1 cm (since the total right vertical length is 3 cm and the left side is divided into 2 cm and 1 cm).

Now, let's calculate the perimeter:

Perimeter=6cm+3cm+4cm+2cm+2cm+1cm=18cm\text{Perimeter} = 6 \, \text{cm} + 3 \, \text{cm} + 4 \, \text{cm} + 2 \, \text{cm} + 2 \, \text{cm} + 1 \, \text{cm} = 18 \, \text{cm}

So, the perimeter of the shape is 18 cm.

Would you like more details on how the calculation was made, or do you have any questions?

Here are five related questions for further practice:

  1. How would you calculate the area of the same shape?
  2. If each side length was doubled, what would be the new perimeter?
  3. How would the perimeter change if the length of one side was increased by 2 cm?
  4. What is the difference in perimeter between this shape and a rectangle of dimensions 6 cm by 3 cm?
  5. Can you describe the relationship between the perimeter and area for this shape?

Tip: When calculating the perimeter of composite shapes, ensure all side lengths are accounted for, including those that are not directly labeled but can be inferred from the given dimensions.

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Math Problem Analysis

Mathematical Concepts

Geometry
Perimeter Calculation
Composite Figures

Formulas

Perimeter = Sum of all side lengths

Theorems

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Suitable Grade Level

Grades 5-7