A car's rear windshield wiper rotates 125°. The total length of the wiper mechanism is 20 inches and the length of the wiper blade is 11 inches. Find the area wiped by the wiper blade. (Round your answer to one decimal place.)

To find the area wiped by the wiper blade, we need to calculate the area of the sector of a circle. The sector's radius is the length of the wiper blade, and the angle of the sector is 125°. Here are the steps:

### Step 1: Understand the Geometry
- The wiper blade sweeps a sector of a circle.
- The angle of the sector, \( \theta = 125^\circ \).
- The radius of the sector is the length of the wiper blade, \( r = 11 \) inches.

### Step 2: Convert the Angle to Radians
To find the area of a sector, the angle should be in radians:
\[
\theta \text{(in radians)} = \theta \times \frac{\pi}{180} = 125^\circ \times \frac{\pi}{180}
\]

### Step 3: Area of the Sector Formula
The area \( A \) of a sector of a circle is given by:
\[
A = \frac{1}{2} \times r^2 \times \theta
\]
where \( r = 11 \) inches and \( \theta \) is in radians.

### Step 4: Calculate the Area
Let’s calculate the area now.The area wiped by the wiper blade is approximately **132.0 square inches**.

Would you like more details, or do you have any questions? Here are 5 related questions:

1. How would the area change if the wiper blade were longer?
2. What would be the area wiped if the wiper's angle was 90° instead of 125°?
3. How does changing the length of the wiper blade affect the area wiped?
4. What if the windshield wiper mechanism was 15 inches instead of 20 inches—would that affect the area calculation?
5. Can you derive the general formula to find the area wiped by a wiper of any length and angle?

**Tip:** Remember that increasing the angle or the length of the wiper blade increases the area wiped, but they do so at different rates.

Learn how to calculate the area wiped by a car's rear windshield wiper with a 125° rotation and an 11-inch blade. Understand the geometry involved in the sector of a circle and the formula used for area calculation. Suitable for high school students studying geometry and trigonometry.

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