10. Find the area of the sector PQ.
The angle of the middle of PQ is 120* and it has a side length of 14m
Answers: Pick One
29.3 m^2
101.2 m^2
301 m^2
205.25 m^2
To find the area of the sector PQ, we first need to calculate the area of the full circle. The formula for the area of a full circle is A = πr^2, where r is the radius.
Since the side length is given as 14m, the radius of the circle (which is the distance from the center to the midpoint of PQ) is half of this length, so r = 7m.
Therefore, the area of the full circle is A = π(7)^2 = 49π square meters.
Next, we need to calculate the area of the sector. Since the angle of the sector is 120 degrees, this sector represents 120/360 = 1/3 of the full circle.
So, the area of the sector PQ is 1/3 of the area of the full circle, which is (1/3)*49π = 49π/3 square meters ≈ 51.45 square meters.
Therefore, the correct answer is not included in the options provided. The closest answer would be 29.3 m^2, but that is not the correct area.