Question

Tanika is wrapping a gift both of these containers will hold her gift which container would allow her to use the least amount of wrapping paper explain your reasoning

Answer 1

To find which container would use the least amount of wrapping paper, we need to find the surface area for each container.

The first container represents the figure of a triangular prism.

The formula for the surface is if given by:

`SA=(Perimeter\cdot Lenght)+(2\cdot Base\text{ area)}`

The base area of the two triangles bases:

`=2((base\cdot height))/(2)`

Then:

`=(base\cdot height)`

The perimeter of the base:

= 7cm + 7 cm+10cm

=24 cm

The length of the prism = 30 cm

Replacing these values on the surface area formula:

Then, the surface area for the triangular prism is:

SA = 770 cm²

Now, the second figure presents a rectangular prism.

Where the surface area is given by :

`SA=2((Length\cdot Breadth)+(Breadth\cdot Height)+(Length\cdot Height))`

In this case:

Lenght = 30cm

Height =10cm

Breath = 5cm

Replacing on the formula:

`SA=2((30\cdot5)+(5\cdot10)+(30\cdot10))`

Then:

SA = 1000cm²

Hence, the first figure which represents the triangular prism will allow Tanika to use the least amount of wrapping paper.