Question

Find the area of each triangle. Leave your answer in simplest radical form. **Show work & explain the work to me in proper English, so I know how to do the problem** Picture will be drawn so be patient. Medal will be rewarded for you patronage! :D

Answer 1

use pythagoras's theorem
\[third~ side=\sqrt{6^{2}-3^{2}}=\sqrt{36-9}=\sqrt{27}=\sqrt{9*3}=3\sqrt{3}\]
area of triangle\[=\frac{ 1 }{ 2 }*base*height=\frac{ 1 }{ 2 }*3*3\sqrt{3}=\frac{ 9\sqrt{3} }{ 2 }~sq.~units.\]