Find the area of ​the shaded region.

Question

Given, $MT=2$ and $AC=8$. Calculate the area of ​​the shaded region.

$\triangle BMT_(notable)\implies (a, 2a, a\sqrt5)\\ \therefore MT = 2, BT=4\\ \triangle ABF \sim \triangle MBT \implies k = \frac{MT}{BT }=\frac{1}{2} =\frac{AF}{BF}\therefore AF =2.2 = 4, BF = 2.4 = 8 \\ S\triangle AMC = S\triangle MCB$

Missing a detail,,,

I managed to solve

Answer 1

$MT=2, BT = 4, BM = 2\sqrt5\\ \triangle AGC \sim \triangle MTB\\ \frac{GC}{TB}=\frac{AC}{MB}\\ \frac{GC}{4}=\frac{8}{2\sqrt5}\\ ∴GC=\frac{16}{\sqrt5}\\ S_{\triangle MBC} =\frac{1}{2}.MB⋅GC=\frac{1}{2}\cdot 2\sqrt5 \cdot \frac{16}{\sqrt5}=16$