The given figure is a regular hexagon with side length 12 and radius 10. Find the length of the apothem a. Question 16 options: A) 15.6 B) 8 C) 12 D) 9

the length of the apothem is 8, option B

Step-by-step explanation:

given:

a regular hexagon with side length 12 and radius 10.

find;

the length of the apothem

referring to the attached image,

to get the length of the apothem, use the Pythagorean theorem.

a² + b² = c²

let a = 6, b = apothem, c = 10

plugin values into the formula

6² + b² = 10²

b² = 10² - 6²

b =

b =

b = 8

therefore,

the length of the apothem is 8, option B

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

it's d

step-by-step explanation: