ANSWER
[tex]35.76in^2[/tex]EXPLANATION
The hypotenuse of the triangle is 12 inches and one leg is 8 inches.
The area of a triangle is:
[tex]\begin{gathered} A=\frac{1}{2}\cdot b\cdot h \\ b=\text{base; h}=\text{height} \end{gathered}[/tex]To find the area of the triangle, find the other leg first: using Pythagoras Rule:
[tex]\begin{gathered} hyp^2=a^2+b^2 \\ a,b\text{ =legs of triangle} \\ \Rightarrow12^2=8^2+x^2 \\ 144=64+x^2 \\ x^2=144-64=80 \\ x=\sqrt[]{80} \\ x=8.94in \end{gathered}[/tex]Find the area of the triangle:
[tex]\begin{gathered} A=\frac{1}{2}\cdot8\cdot8.94 \\ A=35.76in^2 \end{gathered}[/tex]That is the area of the triangle.
