根据勾股定理:(b/2)^2 + h^2 = a^2
h = √{a^2 - (b/2)^2} = √{6+√3)^2 - (3+2√3)^2} = √18 = 3√2
S=1/2bh = 1/2×(6+4√3)× 3√2 = 9√2 + 6√6