a sector with a central angle measure of 7pi/4 in radians has a radius of 16cm what is the area of the sector

The area of this sector is 224*pi cm² or approximately 703.72 cm²

Step-by-step explanation:

In order to calculate the area of a sector for which we have an angle in radians, we need to apply a rule of three in such a way that pi*r² is related to 2*pi radians in the same proportion as the given angle is related to the area of the sector we want to find. This is shown below:

2*pi rad - > pi*r² unit²

angle rad - > sector area unit²

2*pi / angle = pi*r² / (sector area)

2*pi * (sector area) = pi*r²*angle

sector area = [pi*r²*angle]/2*pi

sector area = r²*angle/2 unit²

Applying the data from the problem, we have:

sector area = [ (16) ² * (7*pi/4) ]/2 = [256 * (7*pi/4) ]/2 = 64*7*pi/2 = 32*7*pi = 224*pi

sector area = 224*pi cm²

sector area = 703.72 cm²