In circle M with m, angle, L, M, N, equals, 102, degreesm∠LMN=102
∘
and L, M, equals, 19LM=19, find the area of sector LMN. Round to the nearest hundredth.
To find the area of sector LMN, we need to use the formula:
Area of sector = (angle measure/360 degrees) * πr²
First, we need to find the radius of circle M. Since LM = 19, we know that the radius is half of that, so r = 19/2 = 9.5.
Now let's calculate the area of sector LMN:
Area of sector = (102/360) * π(9.5)²
= (0.2833) * π(90.25)
≈ 0.2833 * 283.91
≈ 80.49
Rounding to the nearest hundredth, the area of sector LMN is approximately 80.49 square units.