You can break the shape up into a rectangle and a right triangle.
Use your trig ratios to find the missing sides.
Add all the sides up and you have your perimeter!
//
[tex]p = 2(l) + 2(w)[/tex]
[tex]p = 2(10) + 2(4)[/tex]
[tex]p = 28[/tex]
//
[tex]tan = \frac{opp}{adj} [/tex]
[tex] \tan(45) = \frac{10}{adj} [/tex]
[tex]adj = \frac{10}{ \tan(45) } [/tex]
[tex]adj = 10[/tex]
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {10}^{2} + 10 {}^{2} = {200}^{2} [/tex]
[tex] \sqrt{200} = 14.14213562[/tex]
//
[tex]p = 10 + 4 + (4 + 10) + 14.14213562[/tex]
*notice how one of the 10 is left out because it is inside the shape so we can't use that to find perimeter.
[tex]p = 42.14[/tex]
