ANSWER
[tex]Area = 2\sqrt{3} \: {cm}^{2} [/tex]
EXPLANATION
We need to use the Pythagoras Theorem to find the height of the triangle.
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] ({2 \sqrt{3}) }^{2} + {b}^{2} = {4}^{2} [/tex]
[tex]12 + {b}^{2} = 16[/tex]
[tex] {b}^{2} = 16 - 12[/tex]
[tex]{b}^{2} = 4[/tex]
Take positive square root to get;
[tex]b = \sqrt{4} = 2[/tex]
Area =½bh
[tex]Area = \frac{1}{2} \times 2\sqrt{3} \times 2[/tex]
[tex]Area = 2\sqrt{3} \: {cm}^{2} [/tex]
