This is known as Einstein's proof, not because he was the first to come up with it, but because he came up with it as a 15 year old boy.
Here the problem is justification step 2. The written equation
BC ÷ DC = BC ÷ AC
is incorrect, and wouldn't get us our statement 2, which is correct.
For similar triangles we have to carefully pair the corresponding parts to get our ratios right:
ABC ~ BDC means AB:BD = BC:DC = AC:BC so BC/DC=AC/BC.
Justification 2 has the final division upside down.
18 feet = 18/3 yard = 6 yard
6 inches = 1/2 feet = 1/6 yard
Volumen = (6yar)(6yard)(1/6yard) = 6 cubic yard
Cost = 6 cubic yard * $42.00 / cubic yard = $ 252.00
Answer: the first option, 252.00
Check the picture below.
make sure your calculator is in Degree mode.