Question

The seating area in a theator is on the shape of a trapezoid. The stage is 5p ft across in the front and in the back 70 ft wide. The seating area is 65 ft deep.What is the area of the seating area

Answer 1

Part a) The area of the seating area is
`3,900\ ft^2`

Part b) The area of the stage is
`1,674\ ft^2`

Explanation:

The complete question is

The seating area in a theater is in the shape of a trapezoid.

The stage is 50 feet across at the front; the back row of seats is

70 feet wide. The seating area is 65 feet deep. What is the area of

the seating area?

b. The stage is also in the shape of a trapezoid. It is 50 feet wide at

the front and 43 feet wide at the back. The stage is 36 feet deep.

Find the area of the stage

see the attached figure to better understand the problem

we know that

The area of a trapezoid is equal to

`A=(1)/(2)(b_1+b_2)h`

where

b_1 and b_2 are the length side of parallel bases

h is the height or deep of trapezoid

Part a) In this problem we have

`b_1=50\ ft`

`b_2=70\ ft`

`h=65\ ft`

substitute in the formula

`A=(1)/(2)(50+70)65`

`A=3,900\ ft^2`

Part b) In this problem we have

`b_1=43\ ft`

`b_2=50\ ft`

`h=36\ ft`

substitute in the formula

`A=(1)/(2)(43+50)36`

`A=1,674\ ft^2`