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:
[tex]SA=(Perimeter\cdot Lenght)+(2\cdot Base\text{ area)}[/tex]
The base area of the two triangles bases:
[tex]=2\frac{(base\cdot height)}{2}[/tex]
Then:
[tex]=(base\cdot height)[/tex][tex]=10\operatorname{cm}\cdot5\operatorname{cm}[/tex][tex]=50\operatorname{cm}[/tex]
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:
[tex]SA=(24\operatorname{cm}\cdot30\operatorname{cm})+50\operatorname{cm}[/tex]
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 :
[tex]SA=2((Length\cdot Breadth)+(Breadth\cdot Height)+(Length\cdot Height))[/tex]
In this case:
Lenght = 30cm
Height =10cm
Breath = 5cm
Replacing on the formula:
[tex]SA=2((30\cdot5)+(5\cdot10)+(30\cdot10))[/tex]
Then:
SA = 1000cm²
Hence, the first figure which represents the triangular prism will allow Tanika to use the least amount of wrapping paper.
