To round the area of the sector to two decimal places, we need to approximate the value of \(\pi\) (approximately \(3.14159\)) and perform the calculations. We have the exact area as:

\[ A = \frac{135\pi}{4} \]

First, let's calculate \( \frac{135}{4} \):

\[ \frac{135}{4} = 33.75 \]

Now, multiply this result by \( \pi \):

\[ A = 33.75 \times 3.14159 \]

Perform the multiplication:

\[ A \approx 33.75 \times 3.14159 \approx 106.0243125 \]

Round this result to two decimal places:

\[ A \approx 106.02 \]

So, the area of the sector, rounded to two decimal places, is approximately:

\[ 106.02 \text{ square feet} \]

Would you like more details on any step or have any questions?

Here are 8 related questions for further practice:
1. What is the circumference of the entire circle with a diameter of 18 feet?
2. How would the area of the sector change if the angle were \( \frac{\pi}{3} \) radians?
3. If the angle of the sector were doubled, what would be the new area?
4. How would you find the length of the arc of this sector?
5. What is the area of the entire circle?
6. How does the area of the sector compare to the area of the entire circle?
7. If the radius were 12 feet and the angle remained \( \frac{5\pi}{6} \), what would be the area of the sector?
8. How would you convert the angle from radians to degrees?

**Tip:** When performing calculations involving \(\pi\), use a sufficiently precise value of \(\pi\) (like 3.14159) to ensure accuracy, especially before rounding.

Learn how to calculate the area of a sector rounded to two decimal places with a step-by-step solution. This problem involves geometry concepts including the calculation of sector areas and the use of precise π (approximately 3.14159). Suitable for high school students.

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