This pentagon is irregular
See the image

We can break this up into 3 triangles AED , ADC and ABC
I'm going to describe how to find the area of triangle AED.....based on this you should be able to figure the areas of the other two triangles ( I'm going to express roots as decimals to ease the computations.....because of this your computation will be a close approximation of the true area )
Find the side lengths using the distance formula
AE = sqrt [ (1 - -3)^2 + (7-4)^2 ] = 5
DE = sqrt [ (-1- -3)^2 + (4 - - 1)^2 ] = sqrt [ 29 ] ≈ 5.39
AD = sqrt [ ( 1- -1)^2 + (7 - -1)^2 ] = sqrt [80 ] ≈ 8.25
Add the sides and divide by 2 = [ 5 + 5.39 + 8.25] / 2 = 9.32
Using Heron's Formula to calculate the area we have
sqrt [s * ( s -AE)(s - DE) (s - AD) ] = sqrt [ 9.32 * (9.32 - 5) (9.32 -5.39) (9.32 - 8.25) ] ≈ 13 units^2
Follow the same procedure for the other two triangles .....
Then....add the ares you get to find the area of the pentagon