A platter is in the shape of a regular octagon. Find the perimeter and area of the platter if the apothem is 6 inches.

Perimeter of platter is 39.84 inch.

Area of platter is

Step-by-step explanation:

Apothem is the perpendicular line from center to the side of the octagon. Given that apothem is 6 inch that is AB=6 inch and (Refer attachment).

Assume DB = BC = x.

Since   is central angle, Therefore  

Since apothem AB bisects angle DAC. So,  

To find the value of BC, use trigonometry ratio for tan for ,

Solving for x multiply whole equation by 6.

Now, DC = DB + BC

Therefore, side of octagon is 4.98 inch .

Perimeter of octagon is,

Since octagon has 8 sides, so number of side is 8

Therefore, perimeter of platter is 39.84 inch.

Area of octagon is,

Therefore, area of platter is

Note: Values are calculated using two decimal places)

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.

hello from mrbilldoesmath!

answer:   x^2 + y^2 = 1024

discussion:

the equation of a circle with center (h,k) and radius "r" is

(x-h)^2 + (y-k)^2 = r^2.

in our case

(x-0)^2 + (y-0) ^2 = 32^2 = 1024

you,

mrb