11. find the area of each regular polygon. round your answer to the nearest tenth. show your work.

a. octagon with side lengths 5in.

b. hexagon with radius 5in

Formula for area of an octagon using a side length is (2+(sqrt2)/2)*s^2 so plugging in 5 will get you about 120.71

with a hexagon, since you dont have a side length you need to create a triangle using the radius. since this is a regular hexagon, each interior angle will be 60 but you have to cut this in half since you are making an angle towards the center of the circle which is where the radius would connect. with this you can create a right triangle that has angles 30, 60, and 90 with the radius of 5 being opposite angle 30. either using pythagoreans theorem or knowing special right triangles you will find that the side opposite 60 is 5*sqrt3. multiply this by 2 to find the side length of the hexagon then plug this in the the formula (1.5*sqrt3)*s^2 to get about 779.42