Answer:
280 ft
Step-by-step explanation:
An auditorium is in the shape of an equilateral triangle with side length as 112 ft.
The stage extends from one vertex of the triangle to the mid-segment and the seating area extends from the mid-segment to the rear wall.
*The situation is represented in the attachment.
According to the midpoint theorem, the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.
Hence, the length of the mid-segment in this case is,
[tex]\dfrac{1}{2}\times 112=56\ ft[/tex]
Therefore, the perimeter of the seating area is,
[tex]=112+56+56+56=280\ ft[/tex]
