Agate is made up of a rectangle and a semicircle as shown. tuan wants to put a trim only along the edges of the gate. how much trim does he need?

c.  32.56 ft

The circumference C of a circle in terms of its diameter d is ...

  C = πd

Then the length of half a circle of that diameter will be ...

  C/2 = (π/2)d

The total length of trim needed is ...

  perimeter = 2 × rectangle sides + rectangle bottom + half-circle top

  = 2 × 6 + 8 + (π/2) × 8

  perimeter = 20 + 4π ≈ 32.56637 . . . . . feet

  ≈ 32.57 ft . . . . . most closely matches option C

Comment on the answer mismatch

It is common on some homework web sites to see the requirement "use 3.14 for π." This is an approximation good only to 3 significant digits, so any answer obtained using this value can only be good to 3 significant digits.

As here, the problem requirement often is for an answer of 4 or more significant digits. The value 3.14 for π is inappropriate in such cases, and gives wrong answers. (The computer may say they're the right choice, but they're not the solution to the problem.)

Here, for example, if Tuan obtains only 32.56 ft of trim, he will be short a small amount and unable to finish his project completely.

step-by-step explanation: