A circle is a curve sketched out by a point moving in a plane. The area of sector BEC when CE = 9 yd is 84.823 yds².
How to find the area of a sector of a circle?
The sector of a circle is like a slice of a circular pizza. Its two straight edge's having an angle, and the edge's length(the radius of the circle) are two needed factors for finding the area of that sector.
Since the whole circle with radius 'r' units have 360 degrees angle on the centre of the circle, and its area is
πr² unit², thus, as the angle lessens, this area gets lessened.
360 degree => πr² unit²
[tex]\rm area\ 1 degree = \pi r^2 \: \rm unit^2/360 area\\\\x\ degree = \dfrac{x \times \pi r^2}{360} \: \rm unit^2 area[/tex]
Thus, the area of a sector with edge length 'r' units and interior angle 'x' degrees is given as:
[tex]A = \dfrac{x \times \pi r^2}{360} \: \rm unit^2 area[/tex]
Given the length of the radius of the circle, CE is 9 yds. Also, the measure of the ∠BEC at the centre of the circle is 120°. Therefore, the area of sector BEC can be written as,
Area BEC = π × r² × (θ/360°)
= π × 9² × (120° / 360°)
= 84.823 yds²
Learn more about the Area of a Circle:
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