Solve ABC. Round to the nearest
tenth if necessary. Use law of sines.

a =  5.2 units, c =  11.1 units to the nearest tenth.

m < A = 27 degrees.

Step-by-step explanation:

c / sin 100 = 9 / sin 53

c =  9 * sin 100 / sin 53

c = 11.098.

m <  A = 180 - 153 = 27 degrees.

a / sin 27 = 9 / sin 53

a = 9 * sin 27 / sin 53

a = 5.166.

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!