Calculating Circle Sector and Bounded Region Areas

TLDR; Calculating the area of sectors and regions bounded by a chord and an arc using central angles and trigonometric functions.

Determining the area of a sector of a circle with a radius of 8 feet and a central angle of 110 degrees.

Using the formula: Area = 1/2 x (R) squared x theta, where theta is the radian measure of the central angle.

Converting 110 degrees to radians by multiplying by pi divided by 180 degrees.

Calculating the area using the given values and determining it to be approximately 61.4 square feet.

Determining the area of a green shaded region in a circle with a radius of 12 centimeters and a central angle of 80 degrees.

The process involves calculating the area of the entire sector and subtracting the area of a triangle within it.

Using the formula for the area of a triangle: Area = 1/2 x (A) x (B) x sine (C), where C is the angle included by side A and side B.

Converting 80 degrees to radians to determine the area of the sector and using the calculated values to find the area of the green region.