Question

Quadrilateral ABCD in the figure below represents a scaled-down model of a walkway around a historic site. Quadrilateral EFGH represents the actual walkway. ABCD is similar to EFGH.

Two irregular similar quadrilaterals ABCD and EFGH are drawn. AB measures 5 inches, BC measures 4 inches, CD measures 4 inches and AD measures 3 inches. EF measures 45 feet.

What is the total length, in feet, of the actual walkway?

Answer 1

when polygons are similar, their sides are proportional.
can you observe that AB and EF are 'corresponding' sides ?

Answer 2

yes! i was thinking the ration would be 9:1..?

Answer 3

not exactly, but "numerically" yes!

Answer 4

like 5in became 45 ft *not 45in*

Answer 5

*shocked* YYYAAAYY! i was 1/2 right :))

Answer 6

oh. you're right..

Answer 7

lol, yes!
so you can find all other sides now ?

Answer 8

would i just multiply 9 to each side.?

Answer 9

exactly.

Answer 10

okay. great! even if the units are different.?

Answer 11

if you wish to use a mathematical equation for 'corresponding sides being proportional' then,
\(\large \dfrac{EF}{AB}=\dfrac{45}{5}=\dfrac{EH}{AD}=\dfrac{HG}{DC}=\dfrac{GF}{CB}=9\)

Answer 12

once i have all the sides, i then find the area.?

Answer 13

maintain the units,
like for GF = 9*CB = 9*4 = 36
write that as 36ft and not 36in

Answer 14

alright. do you mind if i get back to you with my answer to make sure it's all good.?

Answer 15

sure!
i mean i don't mind :)

Answer 16

thank youu! and would i have to use the area of a trapezoid for this one.? @hartnn

Answer 17

"What is the total length, in feet, of the actual walkway? "
you don't need area :P

Answer 18

ok. so add it all up..?

Answer 19

total length of walkaway = perimeter of walkaway.

Answer 20

yes, perimeter is just sum of sides :)

Answer 21

would it be 144.? @hartnn

Answer 22

144 " ft " is correct! :)
i just got a shorter way to do it :P

Answer 23

since the sides are 9 times larger, just add up sides of smaller triangle and multiply by 9 !
9 (3+4+4+5) = 144

Answer 24

**smaller polygon

Answer 25

and why didn't you tell me this earlier -_-..?

Answer 26

LOL!!

Answer 27

however i feel victorious, so I don't know XD

Answer 28

lol, because i "just" got that idea.
anyways, the whole point of this problem was to practice, "corresponding sides of similar polygons are proportional", so we are good with this method :)

Answer 29

si!! thanks youu!! Your aweosme!

Answer 30

you are awesome learner too! :D
most welcome ^_^