Question

right triangle jkl is inscribed in circle n. find the area of the shaded region. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Identify hypotenuse (diameter)

Right triangle inscribed in circle ⇒ hypotenuse = diameter. Right angle at L, legs JL=11, LK=60. Hypotenuse JK = √(11²+60²)=61 (diameter).

Step2: Calculate circle radius

Radius r = diameter/2 = 61/2 = 30.5.

Step3: Compute circle area

Area of circle = πr² = π(30.5)² = 930.25π ≈ 2922.47.

Step4: Compute triangle area

Area of triangle = (1/2)×11×60 = 330.

Step5: Find shaded area

Shaded area = Circle area - Triangle area ≈ 2922.47 - 330 = 2592.5.

Answer:

2592.5