please help answer

Question

The seating area of an auditorium is shaped like a trapezoid, with front and back sides parallel. The front of the auditorium measures 89 feet across, the back of the auditorium measures 151 feet across, and the auditorium is 200 feet from front to back. If each seat requires a space that is 2.4 feet wide by 2 feet deep, how many seats will the auditorium? hold?

Answer 1

The question is poorly posed.

Marlene S.'s solution works only if the seats are fluid - can be squeezed into the space.

The first row contains 37 seats, 89/2.4 = 37.08333....

The last row contains 62 seats, 151/2.4 = 62.91666...

To determine the number of seats the length of each row must be determined.

Answer 2

Ryan,

 

Begin with the area of a trapezoid.

 

A = h(b₁+b₂)/2

b₁ = 89

b₂ = 151

h = 200

A = (200)(151+89)/2 = 24000

 

Now the area of the space required for each seat is

2.4(2) = 4.8

 

24000/4.8 = 5000

 

This auditorium can hold 500 seats.