Question

Given: AABC, mZACB=90°, CD I AB ,mZACD=60°, BC = 6 cm Find: CD, Area of AABC

Answer 1

Check the picture below.

so, since we know the height of the triangle and its base is simply a + b, then

$\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=\stackrel{a}{9}+\stackrel{b}{3}\\ \qquad 12\\ h=3\sqrt{3} \end{cases}\implies A=\cfrac{1}{2}(12)(3\sqrt{3})\implies A=18\sqrt{3}$