What do you go by for the pattern 360,60,10 would it be add 60, divided by 6 ,multiply by 6 or subtract 300?

divided by 6

Step-by-step explanation:

Given pattern

360,60,10

would it be add 60

lets

add 60 to each term

360 +60 = 420

but next term is 60, hence it incorrect choice

divided by 6

lets divide each term by 6

360/6 = 60 which is the next term in the series as well

60/6 = 10 which is also the next term in the series as well

hence divided by 6 is the correct option.

multiply by 6

multiply by 6 to each term

360 *60 = 21600

but next term is 60, hence it incorrect choice

subtract 60 from each term

360 -300 = 60 which is the next term in the series

60 -300 = -240 which is not same the next term in the series that is 10

hence this is incorrect choice

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!