Two triangular prisms are similar. The perimeter of each face of one prism is double the perimeter of the
corresponding face of the other prism.
How are the surface areas of the figures related?
O The surface areas are the same.
O The surface area of the larger prism is 2 times the surface area of the smaller prism.
O The surface area of the larger prism is 4 times the surface area of the smaller prism.
O The surface area of the larger prism is 8 times the surface area of the smaller prism.

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MrRoyal MrRoyal · Answer 1 · 2021-09-30T01:15:07+02:00

The area of a shape is the amount of space it can occupy.

The surface area of the larger prism is 4 times the surface area of the smaller prism.

Let the dimension of one side of the smaller prism be: l and w

Let the dimension of one side of the bigger prism be: L and W

So, we have:

[tex]L = 2l[/tex]

[tex]W =2w[/tex]

The area of these corresponding sides are:

[tex]A_1 =l \times w[/tex] ---- the first

[tex]A_1 = lw[/tex]

While, the area of the second is:

[tex]A_2 =2l\times 2w\\[/tex]

[tex]A_2 =4lw[/tex]

The ratio of these two sides are:

[tex]Ratio = A_1 : A_4[/tex]

This gives

[tex]Ratio = lw : 4lw[/tex]

Cancel out common terms

[tex]Ratio = 1 : 4[/tex]

Express as fractions

[tex]Ratio = \frac 14[/tex]

Also, we have:

[tex]Ratio = \frac{Small}{Large}[/tex]

This gives

[tex]\frac{Small}{Large} = \frac 14[/tex]

Cross multiply

[tex]Large = 4 \tiimes Small[/tex]

[tex]Large = 4\4Small[/tex]

Hence, option (c) is true