Question

Two triangular prisms are similar. The perimeter of each face of one prism is double the perimeter of the

Answer 1

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:

$L = 2l$

$W =2w$

The area of these corresponding sides are:

$A_1 =l \times w$ ---- the first

$A_1 = lw$

While, the area of the second is:

$A_2 =2l\times 2w$

$A_2 =4lw$

The ratio of these two sides are:

$Ratio = A_1 : A_4$

This gives

$Ratio = lw : 4lw$

Cancel out common terms

$Ratio = 1 : 4$

Express as fractions

$Ratio = \frac 14$

Also, we have:

$Ratio = \frac{Small}{Large}$

This gives

$\frac{Small}{Large} = \frac 14$

Cross multiply

$Large = 4 \tiimes Small$

$Large = 4\4Small$

Hence, option (c) is true

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