Question
This figure consists of a rectangle, a semicircle, and a quarter circle.
What is the perimeter of this figure?
Use 3.14 for π.
Responses
22.55 m
22.55 m
27.55 m
27.55 m
29.70 m
29.70 m
37.55 m
What is the perimeter of this figure?
Use 3.14 for π.
Responses
22.55 m
22.55 m
27.55 m
27.55 m
29.70 m
29.70 m
37.55 m
Answers
Answered by
GPT-4o mini
To find the perimeter of the given shape consisting of a rectangle, a semicircle, and a quarter circle, we need to know the dimensions of each part (the length, width of the rectangle, the radius of the semicircle, and the quarter circle).
Since you haven't provided numerical values for these dimensions, I'll outline the general method to calculate the perimeter:
1. **Rectangle**: The perimeter contribution from the rectangle will depend on the dimensions. For example, if the rectangle has a length \( l \) and a width \( w \), the contribution to the perimeter from just one side is \( l \) (if the other sides are covered by the semicircle and quarter circle).
2. **Semicircle**: The diameter of the semicircle is equal to the width of the rectangle \( w \). The circumference of a full circle is \( 2\pi r \) and for the semicircle, it's half of that:
\[
\text{Semicircle perimeter} = \pi r = \pi \left(\frac{w}{2}\right) = \frac{\pi w}{2}
\]
3. **Quarter circle**: For the quarter circle, if it has a radius \( r \), then its perimeter contribution is:
\[
\text{Quarter circle perimeter} = \frac{1}{4} \times 2\pi r = \frac{\pi r}{2}
\]
Now, to calculate the total perimeter, you will sum the straight edges and the curved edges while ensuring to not double-count any overlapping edges.
The equation will end up looking something like this:
\[
P = l + \text{(perimeter contributions from semicircle + quarter circle)}
\]
Once you substitute the values for \( l \), \( w \), and \( r \), you will calculate the total.
If you give me the dimensions, I can help you find the exact perimeter and select one of the answers you provided.
Since you haven't provided numerical values for these dimensions, I'll outline the general method to calculate the perimeter:
1. **Rectangle**: The perimeter contribution from the rectangle will depend on the dimensions. For example, if the rectangle has a length \( l \) and a width \( w \), the contribution to the perimeter from just one side is \( l \) (if the other sides are covered by the semicircle and quarter circle).
2. **Semicircle**: The diameter of the semicircle is equal to the width of the rectangle \( w \). The circumference of a full circle is \( 2\pi r \) and for the semicircle, it's half of that:
\[
\text{Semicircle perimeter} = \pi r = \pi \left(\frac{w}{2}\right) = \frac{\pi w}{2}
\]
3. **Quarter circle**: For the quarter circle, if it has a radius \( r \), then its perimeter contribution is:
\[
\text{Quarter circle perimeter} = \frac{1}{4} \times 2\pi r = \frac{\pi r}{2}
\]
Now, to calculate the total perimeter, you will sum the straight edges and the curved edges while ensuring to not double-count any overlapping edges.
The equation will end up looking something like this:
\[
P = l + \text{(perimeter contributions from semicircle + quarter circle)}
\]
Once you substitute the values for \( l \), \( w \), and \( r \), you will calculate the total.
If you give me the dimensions, I can help you find the exact perimeter and select one of the answers you provided.