Find the area of the following shape. you must show all work to receive credit. figure abcdef is shown. a is located at 5, 6. b is located at 11, 3. c is located at 11, negative 3. d is located at 4, negative 3. e is located at 5, 3. f is located at 1, 3.

First, we are going to draw a diagram of the shape. Next, we are going to draw a point P(5,3) to divide our shape into three smaller figures: triangles ABF and DEP and square BCPE.
Now we can find the area of our smaller figures.
For triangle ABF
Remember that the area of a triangle is 
where 
is the base of the triangle 
is the height of the triangle 
We can infer from our diagram that the base of our triangle is the measure of  line segment FB; similarly,  the height of our triangle is the measure of the line segment EA. To find the measures of our line segments, we are going to use the distance formula: 

where
are the coordinates of the first point 
are the coordinates of the second point 

Now we can find the area of our triangle:

square units

For triangle DEP
and 

square units 

For square BCPE
Remember that the area of a square is:
where 
one of the sides of the square 
We are going to use the measure of line segment PC here, so . Lets use the distance formula to find the measure of line segment PC:

square units

Finally, we can add the areas of our smaller figures to find the area of our shape:
15 square units+3 square units+36 square units=54 square units

We can conclude that the area of the figure ABCDEF is 54 square units.