First let's split the shape in two, like this:
As you can see, now we have a triangle on the right, the length of the base of this triangle is the length of the bottom side of the original figure minus the lenght of the top side of the original figure, we can find it like this:
b = 100 ft - 70 ft = 30 ft
The height of the triangle "h" equals the height of the rectangle, which is 50 ft, then we can find the length of the missing side a (the hypotenuse of the triangle) by means of the Pythagorean theorem, like this:
[tex]\begin{gathered} a^2=h^2+b^2 \\ a=\sqrt[]{h^2+b^2} \end{gathered}[/tex]
Where "a" is the length of the hypotenuse, "h" is the height and "b" is the base. By replacing 30 for b and 50 for h, we get:
[tex]a=\sqrt[]{50^2+30^2}=\sqrt[]{2500+900}=10\sqrt[]{34}=58.3[/tex]
Then the length of the missing side of the composite shape is around 58.3 ft:
Now that we know the lengths of the sides of this figure we can calculate its perimeter by summing them up, like this:
Perimeter = 70 + 50 + 100 + 58.3 = 278.3
The perimeter of this plot of land equals 278.3 ft
