Question
The area of grass at the town center is 319.04 square feet. this excludes the area of a gazebo. The gazebo has a diameter of 16 ft. what is the area of the gazebo? what is the missing dimension of the town center's lawn?
Answers
Answered by
GPT-4o mini
To determine the area of the gazebo and the missing dimension of the town center's lawn, we can follow these steps:
### Step 1: Calculate the area of the gazebo.
The gazebo is circular, so we can use the formula for the area of a circle:
\[
\text{Area} = \pi r^2
\]
Where \( r \) is the radius of the circle. The diameter of the gazebo is given as 16 feet, so the radius \( r \) is half of that:
\[
r = \frac{16}{2} = 8 \text{ feet}
\]
Now, substituting the radius into the area formula:
\[
\text{Area} = \pi (8)^2 = \pi \cdot 64 \approx 201.06 \text{ square feet} \quad (\text{using } \pi \approx 3.14)
\]
So, the area of the gazebo is approximately **201.06 square feet**.
### Step 2: Find the missing dimension of the town center's lawn.
The total area of the lawn (excluding the gazebo) is provided as 319.04 square feet. To find the total area of the lawn, we add the area of the gazebo to the area of the lawn:
\[
\text{Total Area} = \text{Area of Lawn} + \text{Area of Gazebo}
\]
Substituting the values we have:
\[
\text{Total Area} = 319.04 + 201.06 = 520.1 \text{ square feet}
\]
Now, the lawn is said to exclude the gazebo but does not specify its shape. If we need to find a possible missing dimension, we need to assume a shape. Commonly, if we consider the total area of the lawn as a rectangle, let's denote the dimensions of the rectangle as \( l \) (length) and \( w \) (width).
1. **Assuming dimensions of the lawn**: If we assume it is rectangular, we would require either length or width to find the other. For a specific answer, we would typically need one dimension.
For example, if we hypothesize one of the dimensions of the lawn \( w = 10 \text{ ft} \):
\[
l = \frac{\text{Area}}{w} = \frac{319.04}{10} \approx 31.90 \text{ ft}
\]
Thus, you'd gain a specific dimension depending on additional constraints or features of the lawn's shape.
If you have more information about what kind of shape or size the town center's lawn should be, we can come up with specific dimensions! Would you like to provide any additional context?
### Step 1: Calculate the area of the gazebo.
The gazebo is circular, so we can use the formula for the area of a circle:
\[
\text{Area} = \pi r^2
\]
Where \( r \) is the radius of the circle. The diameter of the gazebo is given as 16 feet, so the radius \( r \) is half of that:
\[
r = \frac{16}{2} = 8 \text{ feet}
\]
Now, substituting the radius into the area formula:
\[
\text{Area} = \pi (8)^2 = \pi \cdot 64 \approx 201.06 \text{ square feet} \quad (\text{using } \pi \approx 3.14)
\]
So, the area of the gazebo is approximately **201.06 square feet**.
### Step 2: Find the missing dimension of the town center's lawn.
The total area of the lawn (excluding the gazebo) is provided as 319.04 square feet. To find the total area of the lawn, we add the area of the gazebo to the area of the lawn:
\[
\text{Total Area} = \text{Area of Lawn} + \text{Area of Gazebo}
\]
Substituting the values we have:
\[
\text{Total Area} = 319.04 + 201.06 = 520.1 \text{ square feet}
\]
Now, the lawn is said to exclude the gazebo but does not specify its shape. If we need to find a possible missing dimension, we need to assume a shape. Commonly, if we consider the total area of the lawn as a rectangle, let's denote the dimensions of the rectangle as \( l \) (length) and \( w \) (width).
1. **Assuming dimensions of the lawn**: If we assume it is rectangular, we would require either length or width to find the other. For a specific answer, we would typically need one dimension.
For example, if we hypothesize one of the dimensions of the lawn \( w = 10 \text{ ft} \):
\[
l = \frac{\text{Area}}{w} = \frac{319.04}{10} \approx 31.90 \text{ ft}
\]
Thus, you'd gain a specific dimension depending on additional constraints or features of the lawn's shape.
If you have more information about what kind of shape or size the town center's lawn should be, we can come up with specific dimensions! Would you like to provide any additional context?
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