Answer :

The Area of sector KLM in circle L is approximately 9.82 square units, rounded to the nearest hundredth.

The area of a sector can be calculated using the formula:

Area of sector = (m∠KLM ÷ 360°) × πr²

First, we need to find the radius of circle L. Since KL is given as 4, the radius is half of that, which is 2.

Next, we can calculate the angle m∠KLM in degrees by subtracting it from 360° (since it is the complement angle):

m∠KLM = 360° - 78° = 282°

Now, we can substitute the values into the formula:

Area of sector = (282° ÷ 360°) × π(2)²

Calculating this, we have:

Area of sector ≈ (0.7833) × 12.57 ≈ 9.82.

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Note the full question may be :

In circle L, given that ∠KLM = 78°, KL = 4, we need to find the area of sector KLM.

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