>>749
出来た。
α={a^2 - b^2 - c^2 + d^2}/{2(ad+bc)}

{sin∠BAD}^2=1-α^2=(1+α)(1-α)
={(a^2 + 2ad + d^2) - (b^2 - 2bc + c^2)}{-(a^2 - 2ad + d^2) + (b^2 + 2bc + c^2)}/{4(ad+bc)^2}
=(-a+b+c+d)(a-b+c+d)(a+b-c+d)(a+b+c-d)/{4(ad+bc)^2}
=(2s-2a)(2s-2b)(2s-2c)(2s-2d)/{4(ad+bc)^2}
=2(s-a)(s-b)(s-c)(s-d)/{(ad+bc)^2}

S={ad*sin∠BAD}/2 + {bc*sin∠BCD}/2
=(ad+bc)sin∠BAD
={(s-a)(s-b)(s-c)(s-d)}^(1/2)