Apatio in the shape of a regular octagon (8-sided figure) has a side length of 24 ft and an apothem length of 60 ft. what is the patio’s area?

Method 1
Slide=24 ft
apothem=60 ft

Área=(1/2)*8*s*a
Area(octagon)=(1/2)*8*24ft*60ft=5760 ft²

Solution:  5760 ft²    

Note:

Really, this octagon don´t exist, an octagon with a side length of 24 ft have an apothem length of  28,97 feet.
tg 22.5=12 feet / a  ⇒a=12 feet / tg22.5=28,97 feet

This problem is wrong.  An octagon with side length of 24 ft, it will an apothem with 28,97 feet.