A flagpole casts a shadow of 34 ft. At the same time, a 5 ft. man casts a shadow of 4 ft. What is the height of the flagpole?

We need to find the area of the semicircles + the area of the square.

The area of a square is equal to the square of the lenght of one side.

As = L^2 = 58m^2 = 3,364 m^2

Now, each of the semicircles has a diameter of 58m, and we have that the area of a circle is equal to:

Ac = pi*(d/2)^2 = 3.14*(58m/2)^2 = 3.14(27m)^2 = 2,289.06m^2

And the area of a semicircle is half of that, so the area of each semicircle is:

a =  (2,289.06m^2)/2 = 1,144.53m^2

And we have 4 of those, so the total area of the semicircles is:

4*a = 4* 1,144.53m^2 = 4578.12m^2

Now, we need to add the area of the square 3,364 m^2 + 4578.12m^2 = 7942.12m^2

This is nothing like the provided anwer of Val, so the numbers of val may be wrong.