lua, 126 bytes

Result

WA

Duration

549ms

Code [DL]

X={}
x=0
for i=-3,8 do
X[i]=io.read"*n"-(X[i%3-3]or 0)
p=-~i%3
q=~-i%3
x=x+i//6*X[i]*(X[p]*X[q+3]-X[q]*X[p+3])
end
print(x//6)

stdin

23 69 35
86 03 50
95 96 42
75 02 78

stdout

stderr

/usr/bin/lua5.3: /volume/CODE:7: attempt to perform arithmetic on a nil value (field '?')
stack traceback:
	/volume/CODE:7: in main chunk
	[C]: in ?

strace