I worn down counting all the rectangles I can see, yet that didn"t work. How do I technique this?

Go action by step.

First Picture: 1 rectangle

Second Picture: 2 extr rectangles. The small rectangle, which has been included and the huge one, which includes the two small rectangles.

You are watching: How many four-sided figures

Third picture: The large rectangle. Then two rectangles, which includes 2 little linked rectangles. And the little rectangle, which has actually been added

Fourth picture: only one tiny rectangle.

Fifth Picture: The rectangle, which includes the two tiny rectangle and the tiny additional rectangle.

You go on favor this. Then sum the quantity of rectangles.

share
cite
monitor
answer Jul 20 "14 in ~ 15:34

callculus42callculus42
\$endgroup\$
4
\$egingroup\$
Each rectangle has actually two upright lines and two horizontal lines.

There are five vertical present in the picture, we deserve to label lock 1, 2, 3, 4, 5.

If the outward edge is 1: then the top and also bottom room uniquely determined, and also it is simple to see that 3 or 4 need to be the best edge. 2 options.

If the leftmost edge is 2: then the rightmost edge is 3 or 4 (2 choices), and also in either situation there are 3 horizontal segments that can serve as the top/bottom(\$inom32 =3\$ choices). So this provides \$2 cdot 3 = 6\$. 6 options.

If the leftmost edge is 3: If the rightmost leaf is 5 there is just one rectangle. If the rightmost sheet is 4, there are 5 horizontal segments for top and bottom, for this reason \$inom52 = 10\$ choices. Therefore 11 options.

If the leftmost edge is 4: then the rightmost leaf is 5, and also there are four horizontal segments yielding \$inom42 = 6\$ feasible rectanges. 6 options

The full is 2 + 6 + 11 + 6 = 25.

See more: Are Rabbits Herbivores Carnivores Or Omnivores ? Are Rabbits Herbivores, Omnivores Or Carnivores

re-publishing
cite
monitor
reply Apr 8 "16 in ~ 22:41

Alex ZornAlex Zorn
\$endgroup\$
Highly active question. Earn 10 call (not counting the combination bonus) in order come answer this question. The reputation necessity helps protect this inquiry from spam and non-answer activity.

## Not the prize you're spring for? Browse various other questions tagged combinatorics or questioning your very own question.

The Overflow Blog
Featured ~ above Meta
2
How many triangles in picture? Formula or algorithm because that this?
related
1
counting words with subset limitations
0
exactly how to tell if ns am twin counting in a combinatorics problem?
1
Counting difficulty involving 3D rotation
1
How countless rectangles deserve to be obtained by joining 4 of the \$12\$ vertices the a \$12\$-sided regular polygon?
0
A rectangle is divided up in the diagram below. How numerous rectangles exist in this diagram?
0
Product dominance of count Strategies inquiry
2
counting lattice routes using all 4 directions
0
How numerous numbers space there that 5 figures..
11
How countless different numbers can be developed with a continual polygon of \$n\$ vertices and also a number \$d\$ the diagonals the this polygon?
hot Network concerns much more hot inquiries
concern feed

smashville247.netematics
agency
ridge Exchange Network
site design / logo design © 2021 ridge Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.10.29.40598

smashville247.netematics ridge Exchange works finest with JavaScript permitted

her privacy

By clicking “Accept all cookies”, you agree stack Exchange can store cookies on your machine and disclose info in accordance through our Cookie Policy.