Question

Paco's building a glass GreenhouseA) how many glass vases does the greenhouse have? The floor is not glass. B) how much glass does Paco need to buy?C) if glass costs $55 per square metre, how much will the Glass cost Paco? What I'm sumption did you make

Answer 1

Given the glass greenhouse, you can identify that it is a triangular prism.

a) You know that floor is not glass.

Notice in the picture that the glass greenhouse has two equal triangular glass faces and two equal rectangular glass faces. Therefore, it has a total of four glass faces.

b) In order to calculate how much glass he needs to buy, you need to add the areas of the two equal rectangular glass faces and the areas of the two equal triangular glass faces.

The formula for calculating the area of a rectangle is:

`A_r=lw`

Where "l" is the length and "w" is the width.

And the formula for calculating the area of a triangle is:

`A_t=(bh)/(2)`

Where "b" is the base and "h" is the height.

Therefore, you can write the following equation to represent the total area of glass:

`\begin{gathered} A=2lw+2((bh)/(2)) \\ \\ A=2lw+bh \end{gathered}`

In this case, you can identify that:

`\begin{gathered} l=2.4m \\ w=1.1m \\ \\ b=1.8m \\ h=0.6m \end{gathered}`

Hence, substituting values into the equation and evaluating, you get:

`\begin{gathered} A=2(2.4m)(1.1m)+(1.8m)(0.6m) \\ \\ A=5.28m^2+1.08m^2 \end{gathered}`
`A=6.36m^2`

c) You know that glass costs $55 per square metre. Therefore, you need to multiply this amount of money by the total square meters of glass he needs to buy, in order to find how much the glass will cost Paco:

`(6.36)($\text{ \$}$55)=\text{ \$}349.8`

Hence, the answers are:

a) It has 4 glass faces.

b) He needs to buy:

`6.36m^2`

c) It will cost:

`\text{ \$}349.8`

This quantity can be found by multiplying the square meters of glass Paco needs by the cost of one square meter ($55).