How much glass is needed to construct a hexagonal (6-sided) fish tank? The tank is 4 feet tall and each pane is 11 feet wide. The tank's bottom is not made of glass.

Each side of the hexagon is a rectangle of height 4ft and width 11ft.

The area of each one of these rectangles is:

A = 4ft*11ft = 44ft^2

And a hexagon has 6 faces, so the fish tank will have 6 of these rectangles, then the total area is:

area = 6*44ft^2 = 264 ft^2

We know that the base of the hexagon is not made of glass, but we do not know if the top is made of glass or not.

In the case that the top is not made of glass, the amount of glass needed is 264 ft^2

If the top is made of glass, then we need to add the area of a hexagon of side 11 ft, which is:

a = (3*√3)*(11ft)^2/2 = 314.4ft^2

Then the total area in this case is:

264 ft^2 + 314.4ft^2 = 578.4 ft^2

This is the total amount of glass needed to construct the tank if the top of the tank is made of glass.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2