We can use the cosine rule to find an angle θ:
122=62+82-2(6)(8)cosθ, [cosine rule is c2=a2+b2-2abcosC, so a=6in, b=8in, c=12in, C=θ]
144=36+64-96cosθ,
96cosθ=44, cosθ=11/24,
We need sinθ=√(1-cos2θ)=√455/24, [area=½absinC, a=6in, b=8in, C=θ].
area=½(6)(8)sinθ=√455=21.3in2 to the nearest tenth of an inch.