A goat is tied to the corner of a shed

Question

A goat is tied to the corner of a shed 12 feet long and 10 feet wide. If the rope is 15 feet long, over how many square feet can the goat graze ?

I know that this question has already been asked a number of time, but no matter what I do I cannot find the same answer as the one provided in the textbook. I proceed like in this thread so I have :

$\frac{3}{4}15²\pi + \frac{1}{4}3²\pi + \frac{1}{4}5²\pi = \frac{1}{4}709\pi$

However the answer given by the textbook is $177\frac{1}{4}\pi$.

Am I missing something here or is the textbook wrong ?

Answer 1

In business and the trades, at least before everything went to decimal notation for fractions, you would almost never see someone write a number as (for example) $\frac 52.$ Instead they would write $2\frac12,$ which by convention was read as a single number equal to $2+\frac12.$ This notation is called a mixed fraction. It is highly discouraged in most mathematical settings, but you can still see it used sometimes, especially in old puzzle books.

---

While I was trying not to be U.S.-centric in this answer, I should acknowledge that mixed fractions are still extremely common in the U.S. for many kinds of measurements, and as noted in the comments are seen in some contexts in at least a few other countries.

Answer 2

As far as I can tell you’re answer is fine and the textbook is wrong. Maybe the misprint was $709/4=177 +1/4$. So the answers are typed almost the same.