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Posted by **olav** on Sunday, December 12, 2010 at 9:10am.

Trapezoid EFGH is similar to ABCD, top EH and bottom FG are parallel. EH is the smaller of the two parallel lines. Top EH is 10, other sides are unknown.

Area of ABCD is 9 times larger than EFGH.

What is the perimeter of EFGH ?

- grade 9 math -
**Reiny**, Sunday, December 12, 2010 at 9:44amThe areas of similar figures are proportional to the square of their corresponding sides

since the areas are in the ratio of 9:1

the sides are in the ratio of 3:1

so AD/EH = 3/1

AD/10 = 3/1

AD = 30

Perimeter of ABCD = 165

Perimeter EFGH/Perimeter ABCD = 1/3

Perimeter EFGH/165 = 1/3

perimeter EFGH = 55

- grade 9 math -
**olav**, Sunday, December 12, 2010 at 10:12amI am still lost.

How come the areas of similar figures (trapezoids) are proportional to the squeare of their corresponding perimeters.

- grade 9 math -
**Reiny**, Sunday, December 12, 2010 at 10:33amlet me illustrate with an example

consider the right-angled triange with sides 3, 4, and 5

(easy to find areas of right-angles triangles)

a triangle similar is 12, 16, 20 ( I multiplied each side by 4)

area of smaller = (1/2)(3)(4) = 6

area of larger = (1/2)(12)(16) = 96

notice the ratio of their sides = 1:4

ratio of their areas = 6:96 = 1:16 = 1^2 : 4^2

which is the square of their sides.

now look at the perimeters

per of smaller = 3+4+5 = 12

per of larger = 12+16+20 = 48

notice the ratio of perimeters is 12:48 = 1:4

the same as the ratio of sides

Perimeter is a linear relationship

while area is a second degree relationship

Does that help?

- grade 9 math -
**olav**, Sunday, December 12, 2010 at 11:21amDoes this work for all trapezoids ?

Is this true for all similar enclosed figures ?

Can you help me with my other question posted minutes later than this one ?

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