we know that
The area of a right triangle is equal to
\(Area=\frac{1}{2} (Leg1*Leg2)\)
In this problem
\(Leg\ 1=27.6\ cm \\ Hypotenuse=30\ cm\\ Leg\ 2=?\)
Applying the Pythagorean Theorem
\(Hypotenuse^{2} =Leg\ 1^{2} +Leg\ 2^{2} \\ Leg\ 2^{2}=Hypotenuse^{2}-Leg\ 1^{2}\\ Leg\ 2^{2}=30^{2} -27.6^{2} \\ Leg\ 2^{2}=138.24\\ Leg\ 2=11.76\ cm\)
Find the area
\(Area=\frac{1}{2} (27.6*11.76)\)
\(Area=162.29\ cm^{2}\)
therefore
the answer is
the approximate area of the triangle is \(162.29\ cm^{2}\)
