what is the area of a sector with a central angle of 160 degrees and a diameter of 5.8m? round the answer to the nearest tenth A. 8.1 m^2 B.4.0 m^2 C.47.0 m^2 D.11.7 m^2 2.what is the area of a regular octagon with a side of 8

A = 1/2 r^2 θ = 1/2 * 2.9^2 * (160/180)π = ____

as for the octagon, recall the area of a regular polygon = 1/2 ap
where a is the apothem and p is the perimeter.
The apothem, of course is a = 1/2 s tan(180/n)°
where s is the side length.

Did you know?

Did you know that the area of a sector can be calculated by multiplying half of the square of the diameter with the measure of the central angle, and then dividing by two? In the given example, with a central angle of 160 degrees and a diameter of 5.8m, the calculated area of the sector rounded to the nearest tenth is 8.1 m^2. This calculation can be a useful tool for determining the area of sectors in various contexts, such as in geometry or physics. Additionally, did you know that the area of a regular octagon can be found by multiplying the square of the length of one of its sides by 2 times the square root of 2? In the provided question, with a side length of 8 units, the area of the regular octagon can be calculated as 64 multiplied by 2 times the square root of 2, resulting in an area of approximately 181.02 units squared. This formula is not only useful in geometry but also in architecture and design, where octagons are commonly used.