Math Problem Statement

find the perimeter

Solution

To calculate the perimeter of the given shape, we'll add up the lengths of all its sides.

From the image:

  • The top three horizontal segments measure 18 mm, 8 mm, and 20 mm.
  • The two vertical segments on the right are 23 mm each.
  • The three vertical segments on the left are 45 mm, 23 mm, and 45 mm.
  • The bottom three horizontal segments are 10 mm each.

Now, let's add these up:

  1. Top horizontal sides:

    • 18 mm+8 mm+20 mm=46 mm18 \text{ mm} + 8 \text{ mm} + 20 \text{ mm} = 46 \text{ mm}
  2. Right vertical sides:

    • 23 mm+23 mm=46 mm23 \text{ mm} + 23 \text{ mm} = 46 \text{ mm}
  3. Left vertical sides:

    • 45 mm+23 mm+45 mm=113 mm45 \text{ mm} + 23 \text{ mm} + 45 \text{ mm} = 113 \text{ mm}
  4. Bottom horizontal sides:

    • 10 mm+10 mm+10 mm=30 mm10 \text{ mm} + 10 \text{ mm} + 10 \text{ mm} = 30 \text{ mm}

Finally, sum up all the sides to find the perimeter:

P=46 mm+46 mm+113 mm+30 mm=235 mmP = 46 \text{ mm} + 46 \text{ mm} + 113 \text{ mm} + 30 \text{ mm} = 235 \text{ mm}

So, the perimeter of the shape is 235 mm.

Would you like any further details or explanations?

Here are some related questions:

  1. How would you calculate the perimeter if the shape had more indentations?
  2. What is the perimeter of a shape with similar dimensions but without indentations?
  3. How does the unit of measurement affect the calculation of the perimeter?
  4. What is the difference between finding the perimeter of a 2D shape versus the surface area of a 3D shape?
  5. How would you find the perimeter of a complex polygon with more sides?

Tip: When dealing with complex shapes, break the shape into simpler parts to make calculating the perimeter easier.