Triangle ABL is an isosceles triangle in circle A with a radius of 11, PL = 16, and ∠PAL = 93°. Find the area of the circle enclosed by line PL and arc PL. Show all work and round your answer to two decimal places.

The area of the circle enclosed by line segment PL and circle arc PL is 37.80 square units.

The calculation of the area between line segment PL and circle arc PL is described below:

1) Calculation of the area of the circle arc.

2) Calculation of the area of the triangle.

3) Subtracting the area found in 2) from the area found in 1).

Step 1:

The area of a circle arc is determined by the following formula:

(1)

Where:

- Area of the circle arc.

- Arc angle, in sexagesimal degrees.

- Radius.

If we know that and , then the area of the circle arc is:

Step 2:

The area of the triangle is determined by Heron's formula:

(2)

Where:

- Area of the triangle.

- Radius.

- Length of the line segment PL.

If we know that and , then the area of the triangle is:

Step 3:

And the area between the line segment PL and the circle arc PL is:

The area of the circle enclosed by line segment PL and circle arc PL is 37.80 square units.

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step-by-step explanation: