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Maths Exercices

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 biggest triangular prism?

4 yd

2 yd

182 yd2


S1 = yd2