Answer: The perimeter of the figure is 108 feet.
Step-by-step explanation: The perimeter is the length of the boundary of a closed polygon. In order to figure out the side lengths of this figure so that we can sum them up to find the perimeter, we must use Pythagorean's Theorem.
Pythagorean's Theorem states that the sides of a right triangle can be found via the equation a^2 + b^2 = c^2, where c is the hypotenuse of the triangle and a and b represent the lengths of the other two legs. The figure has been split up into four right triangles, allowing us to perform Pythagorean's Theorem on each triangle in order to figure out the length of each hypotenuse, which correspond to each side length.
For example, one side length can be found by summing 12 squared and 16 squared, which gives you 400. Since 400 represents c squared, all we have to do is find the square root in order to find the hypotenuse length. In this case, the square root of 400 is 20. After finding all the side lengths using this theorem, we simply sum all of them. 20 + 20 + 34 + 34 = 108 feet.
