Geometry

Find the area of the strip.

Let a be the distance of the base 10 touched by the strip.

Let alpha be the slope angle of the strip.

$tan(\alpha)=\frac{8}{10-a}\\ sin(\alpha )=\frac{1}{a}\\ \alpha =atan(\frac{8}{10-a})=asin(\frac{1}{a})\\ atan(\frac{8}{10-a})-asin(\frac{1}{a})=0$

$\color{green}WolframAlpha\\ \color{green}a=\frac{8\sqrt{163}}{63}-\frac{10}{63}\\$

$\color{blue}a=1.4625\\ A=8\cdot 1.4625\\ \color{blue}A=11.7$

$\color{blue}The\ area\ of\ the\ strip\ is\ 11.7\ .$