Finding the Perimeter of an Odd Shape.

In summary, to find the perimeter of an odd shape with a partially rounded edge, you can add the lengths of all the straight edges and half the circumference of the rounded edge. In this case, the perimeter is 16 + 2\pi, where 16 comes from the sum of 7 + 3 + 3 + 3 and 2\pi comes from halving the circumference of the semi-circle.
  • #1
RidiculousName
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I have been looking around for information on how to find the perimeter of an odd shape, but I can't find any explanations that seem to fit because the given shape is partially rounded. I already know the answer is \(\displaystyle 16 + 2\pi\) but I am unsure how they came to it. I'm guessing they get \(\displaystyle 16\) from \(\displaystyle 7 + 3 + 3 + 3\), and \(\displaystyle 2\pi\) by halving the value of the length of the dotted line and multiplying by \(\displaystyle \pi\), but I don't trust myself to guess.

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  • #2
I've edited your post to wrap the expressions containing \pi in [MATH][/MATH] tags. All $\LaTeX$ markup must be wrapped in tags.

The circular arc is half the circumference of a circle whose diameter is 4 units in length. $\pi$ is defined to be the ratio of the circumference $C$ to the diameter $D$ of a circle:

\(\displaystyle \pi=\frac{C}{D}\implies C=\pi D\implies \frac{C}{2}=\frac{\pi D}{2}\)

And so the perimeter $P$ is:

\(\displaystyle P=3\cdot3+7+\frac{\pi\cdot4}{2}=16+2\pi\)
 
  • #3
The bottom has length 7. The straight line portion of the top has length 3. That leaves 7- 3= 4 as the diameter of the semi-circle. The circumference of a full circle is "[tex]\pi D[tex], pi times the diameter- here [tex]4\pi[/tex]. The semi-circle has circumference half that, [tex]2\pi[/tex]. The perimeter of the entire figure is [tex]7+ 3+ 3+ 3+ 2\pi= 16+ 2\pi[/tex].
 

FAQ: Finding the Perimeter of an Odd Shape.

1. How do you define the perimeter of an odd shape?

The perimeter of an odd shape is the total distance around the outer edge of the shape. It is calculated by adding together the lengths of all the sides of the shape.

2. What is the formula for finding the perimeter of an odd shape?

The formula for finding the perimeter of an odd shape varies depending on the shape. For simple shapes such as rectangles or squares, it is the sum of all the sides. For more complex shapes, it may require breaking the shape into smaller, simpler shapes and adding their perimeters together.

3. Can you use a ruler to measure the perimeter of an odd shape?

Yes, you can use a ruler to measure the perimeter of an odd shape. However, for more accurate measurements, it is recommended to use a measuring tape or a digital measuring tool.

4. What are some common mistakes when finding the perimeter of an odd shape?

One common mistake is forgetting to include all the sides of the shape, especially if there are hidden or overlapping sides. Another mistake is using incorrect units of measurement or forgetting to convert between units.

5. How can you check if your calculation of the perimeter of an odd shape is correct?

A good way to check your calculation is to break the shape into smaller, simpler shapes and calculate their perimeters individually. Then, add these perimeters together to see if they match your original calculation. Another way is to use a different method or formula to calculate the perimeter and compare the results.

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