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# Surface Area of Similar Solids

The figures below are similar. What is the surface area of the smaller rectangular pyramid?

The following proportion applies to similar solids:

where is the ratio of the corresponding dimensions, and is the ratio of the surface areas.

Find the square of the ratio of the corresponding dimensions:

Find the ratio of the surface areas:

Use these two ratios to set up a proportion and solve for S1.

=

 9 × 196
=
49
 S1
Find the cross products

1,764 =
49
 S1
Simplify

 1,764 ÷ 49
=
49
 S1
÷ 49
Divide both sides by 49

36 =
 S1

The surface area of the smaller rectangular pyramid is 36 square centimeters. .

The figures below are similar.
What is the surface area of the smaller triangular pyramid?       2 yd    1 yd    11.32 yd 2  S1 = yd2