Question

1. architecture find the amount of glass needed to build the greenhouse. 10 ft 14 ft 8 ft 16 ft 35 ft

Explanation:

Step1: Calculate the area of the two rectangular sides with dimensions \(8\) ft and \(35\) ft

The area of a rectangle is \(A = l\times w\). For each of these sides, \(A_1=8\times35\).
Since there are two such sides, \(A_{total1}=2\times(8\times35)=2\times280 = 560\) square - feet.

Step2: Calculate the area of the two trapezoidal sides

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a = 8\) ft, \(b = 10\) ft, and \(h = 35\) ft.
For each trapezoid, \(A_2=\frac{(8 + 10)\times35}{2}=\frac{18\times35}{2}=9\times35 = 315\) square - feet.
Since there are two trapezoidal sides, \(A_{total2}=2\times315=630\) square - feet.

Step3: Calculate the area of the rectangular top with dimensions \(14\) ft and \(35\) ft

Using the rectangle area formula \(A = l\times w\), where \(l = 35\) ft and \(w = 14\) ft. So \(A_3=14\times35=490\) square - feet.

Step4: Calculate the total area of the glass

The total area \(A=A_{total1}+A_{total2}+A_3\).
Substitute the values: \(A = 560+630 + 490\).
First, \(560+630=1190\), then \(1190+490=1680\) square - feet.

Answer:

The amount of glass needed is \(1680\) square - feet.