Explanation:
the perimeter is the sum of the lengths of all outside sides.
at the top is a triangle.
at the bottom is a rectangle.
the triangle looks like an isoceles triangle (both legs are equal), but the given measurement tells us otherwise.
if it were isoceles, the height would split the baseline into 2 equal halves (20/2 = 10ft).
per Pythagoras the 12 ft Hypotenuse would be
Hypotenuse² = 10² + 10² = 100 + 100 = 200
Hypotenuse = sqrt(200) = 14.14213562... and NOT 12 ft.
so, we need to calculate the actual part of the 20ft baseline (again Pythagoras) :
12² = 10² + part²
144 = 100 + part²
44 = part²
part = sqrt(44) = 6.633249581... ft
that means the 2nd part of the baseline is
20 - 6.633249581... = 13.36675042... ft
and we get the second leg of the large triangle again via Pythagoras :
leg² = 10² + 13.36675042...² = 100 + 178.6700168...
leg² = 278.6700168...
leg = sqrt(278.6700168...) = 16.69341238... ft
we need to sum up both legs of the triangle, 2 widths and one length of the rectangle, as the triangle base line and the second length of the rectangle cover each other up, and are not visible to the outside of the combined object.
P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈
≈ 64.69 ft