Find the area of the following shape. you must show all work to receive credit.

figure abcdef is shown. a is located at negative 5, negative 8. b is located at 1, negative 8. c is located at 3, negative 5. d is located at 1, 0. e is located at negative 5, negative 3. f is located at negative 3, negative 6.

The figure is drawn and partitioned into triangles as shown below.
The coordinates are
A (-5, -8), B (1, -8), C (3, -5), D (1, 0), E (5, -3), and F (-3, -6).

Use the distance formula to calculate the lengths a,b,c,d,e,f,g,h, and k.
a = √[6²+0²] = 6,             b = √[2²+3²] = 3.6056,    c = √[2²+5²] = 5.3852
d = √[4²+3²] = 6.7082,    e = √[8²+3²] = 3.6056,    f = √[2²+2²] = 2.8284
g = √[4²+2²] = 4.4721,     h = √[6²+1²] = 6.0828,     k = √[4²+6²] = 7.2111

The area of a triangle with sides a,b,c is given by
A = √[s(s-a)(s-b)(s-c)]
where s = (1/2)*(a+b+c)
Use this formula to calculate the areas of the partitioned triangles.
Triangle  a           b            c               s             A
ΔABF     6            4.4721   2.8284    6.6503   6
ΔBCF     3.6056  6.0828  4.4721     7.0797    8
ΔCDF     5.3852  7.2111      6.0828   9.3395   16
ΔDEF     6.7082  3.6056   7.2111       8.7625   12

Total area  = 6 + 8 + 16 + 12 = 42

42 square units.