The set of consists of counting numbers, their opposites, and zero.

Integers

Step-by-step explanation: The set of counting numbers (1, 2, 3, 4, 5) is called the set on natural numbers. This set of numbers starts at 0 and goes on indefinitely. When we include 0 in the set of natural numbers, the new set is called whole numbers. (0, 1, 2, 3, 4, 5) If we also include a numbers opposite, then we are dealing with integers. Integers are positive and negative whole numbers, including 0, but they can't be in the form of fractions or decimals. Some examples of integers can be (-25, -5, -16, 73).

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!

22 dimes and 9 nickels

step-by-step explanation: