To find the area of the sector PQ, we need to use the formula for the area of a sector of a circle:
Area = (θ/360) x π x r^2
where θ is the central angle in degrees and r is the radius of the circle.
The central angle given is 120 degrees and the side length of the sector is 14m. To find the radius, we need to use trigonometry. Since the sector is an isosceles triangle with two sides of length 14m, the radius will be half of the diagonal of the sector.
Using the Pythagorean theorem, the diagonal of the sector can be found as:
diagonal = 2 * √(14^2 + 7^2)
diagonal = 2 * √(196 + 49)
diagonal = 2 * √245
diagonal = 2 * 15.65 ≈ 31.3
So, the radius of the circle is half of the diagonal, which is 31.3/2 = 15.65m.
Now we can calculate the area of the sector:
Area = (120/360) x π x (15.65)^2
Area = (1/3) x π x 244.9225
Area ≈ 257.08 m^2
Therefore, none of the provided answer choices is correct. The area of the sector PQ is approximately 257.08 m^2.
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:
29.3 m^2
101.2 m^2
301 m^2
205.25 m^2
1 answer