Jumat, 22 Maret 2013

LAYANG-LAYANG (KITES) DAN TRAPEZOID

A. LAYANG-LAYANG (KITES)

Layang -layang adalah segiempat yang dibentuk oleh dua segitiga sama kaki yang alasnya sama panjang dan berhimpit.

1. Sifat Layang-layang (Properties of Kites)
    a. Mempunyai dua pasang sisi sama panjang.
        AB = BC dan AD = CD
    b. Sepasang sudut yang berhadapan sama besar yakni sudut bagian sayap.
        Sudut BAD = Sudut BCD
    c. Mempunyai satu sumbu simetri yang merupakan diagonal terpanjang.
        Diagonal BD adalah sumbu simetri layang-layang.
    d. Diagonal bagian sayap membagi dua sama panjang dan tegak lurus terhadap diagonal lain.
        OA = OC = 1/2 AC  dan AC tegak lurus BD

2. Keliling dan Luas Layang-layang (Perimeter and Area of Kites)
    a. Keliling layang - layang = panjang keempat sisinya
                                           =   AB + BC + CD + AD

    b. Luas Layang-layang =     

                                                       

B. TRAPESIUM (TRAPEZOID)

Trapesium adalah segi empat yang mempunyai sepeasang sisi berhadapan sejajar.

                

1. Sifat - Sifat Trapesium (Properties of Trapezoid)
   a. Mempunyai sisi yang sejajar
       AB // DC tetapi AB tidak sama panjang dengan DC
   b. Mempunyai dua sudut lancip dan dua sudut tumpul
       Sudut Lancip = Sudut BAD dan Sudut ABC
       Sudut Tumpul = Sudut ADC dan Sudut BCD
   c. Jumlah sudut yang berdekatan di antara dua sisi sejajar ialah 180 derajat.
       Sudut A + Sudut D = 180
       Sudut B + Sudut C = 180

Berlaku khusus untuk trapesium sama kaki:
a. Mempunyai dua pasang sudut yang berdekatan sama besar.
b. Mempunyai dua diagonal yang sama panjang.

2. Keliling dan Luas Trapesium (Perimeter and Area of Trapezoid)
a. Keliling  Trapesium  = AB + BC + CD + AD

b. Luas Trapesium  

                                                          

SOAL-SOAL DAN PEMBAHASAN

1. Nyatakan masing-masing kalimat berikut ini BENAR atau SALAH untuk setiap layang-layang.
    a. Diagonal-diagonalnya sama panjang.
    b. Diagonal-diagonalnya saling berpotongan tegak lurus.
    c. Mempunyai dua pasang sisi yang sama panjang.
    d. Dua sudutnya yang berhadapan sama besar.

JAWAB:
    a. SALAH, diagonal -diagonal pada layang-layang TIDAK sama panjang.
    b.BENAR, diagonal-diagonal pada layang-layang berpotongan tegak lurus di O.
    c. BENAR, karena layang-layang dibentuk dari dua segitiga sama kaki.
    d. BENAR, sudut-sudut pada bagian sayap layang-layang sama besar.

2. Pada layang-layang ABCD berikut, besar sudut DAC  = 30 derajat dan Sudut CDB = 40 derajat.
    Tentukan:
    a. besar Sudut ADB;dan
    b. besar Sudut ABC.

JAWAB:
a. Sudut ADB = 180 - (Sudut AOD + Sudut DAC)
                      = 180 -  (90 + 30)
                      = 180 - 120
                      = 60
b. Sudut ABC = Sudut ADC
                       = Sudut ADB + Sudut CDB
                       = 60 + 40
                       = 100

3. Hitunglah luas layang-layang berikut.
JAWAB:
Diagonal 1 = 5 + 9 = 14 cm
Diagonal 2 = 4 + 4 = 8 cm
Luas Layang-layang  
                                
                                =  56 cm2

4. Luas suatu layang - layang adalah 60 cm2. Jika panjang salah satu diagonalnya 8 cm,
    hitunglah panjang diagonal yang lainnya.

JAWAB:
Luas layang-layang


120 = 8 x d1
d1   = 120 : 8
d1   = 15

Jadi, diagonal yang lain adalah 15 cm.

5. Diketahui luas persegi panjang ABCD pada gambar berikut 432 cm2.
    Luas daerah layang-layang adalah  . . .



JAWAB:
Luas persegi panjang = 3x . 2x
                        432   =
Luas layang - layang =                
                                     
                                  
                               
                               = 216 cm2

6. Pada trapesium sama kaki ABCD, panjang AD = BC, dan besar Sudut A = 65 derajat.
    a. Tentukan besar Sudut B!
    b. Tentukan besar Sudut C dan Sudut D!

JAWAB:
a. Sudut A = 65 derajat maka sudut B juga 65 derajat.
b. Sudut C berdekatan dengan sudut B maka sudut C = 180 - 65 = 115 derajat.
    Karena Sudut A = 65 derajat maka Sudut D pun 115 derajat.

7. Hitunglah luas trapesium berikut ini.
JAWAB:
(i) Luas Trapesium   
                                        
                               = 25 x 6
                              = 150 cm2

(ii) Luas Trapesium         
                           
                                       
                                = 22 x 15
                                = 330 cm2

8. ABCD adalah trapesium siku- siku di A dengan AB//CD.
    Jika besar sudut B : sudut C = 4 : 5,
    tentukan besar sudut-sudut trapesium itu!

JAWAB:
Sudut B dan Sudut C adalah sudut yang saling berdekatan dimana jumlah sudutnya = 180
Jumlah perbandingan adalah 4 + 5 = 9

 
        = 4 x 20  
        = 80

    
        = 5 x 20
        = 100

Jadi, Sudut A = 90, Sudut B = 80, Sudut C = 100 dan Sudut D = 90

9. Perbandingan panjang sisi- sisi sejajar sebuah trapesium adalah 4 : 3.
    Jika tinggi trapesium itu 8 cm, dan luasnya 84 cm2, hitunglah panjang sisi - sisi sejajar tersebut.

JAWAB:
Luas trapesium       
                            

                            
                     
                 a  + b = 21

Jumlah perbandingan sisi-sisi sejajar = 4 + 3 = 7

               
                a  = 4 x 3
                a = 12
           

b = 3 x 3
b = 9

Jadi sisi-sisi yang sejajar pada trapesium itu adalah 12 cm dan 9 cm.

10. Pak Ali membeli sebidang tanah dengan bentuk dan ukuran seperti pada gambar berikut.


Jika harga tanah Rp45.000,00/m2, maka Pak Ali  harus membayar sebesar . . . 

JAWAB:
Untuk menentukan tinggi kita gunakan TEOREMA PYTHAGORAS pada segitiga siku-siku.
Perhatikan gambar.

t  = 10

Luas tanah yang berbentuk trapesium     
                                                            
                                                            = 22 x 10
                                                            = 220 m2
Pak Ali harus membayar  = 220 x Rp45.000,-
                                       =Rp9.900.000,-

















45 komentar:

Anonim mengatakan...

Marvelous, what a webpage it is! This website provides helpful information to us, keep it up.


Have a look at my webpage :: creative entrepreneur ideas

Anonim mengatakan...

I get pleasure from, lead to I found exactly what I was taking a look for.

You've ended my 4 day lengthy hunt! God Bless you man. Have a great day. Bye

Here is my web page bad credit unsecured loans

Anonim mengatakan...

Hi, this weekend is good designed for me, since this occasion i am reading this impressive informative piece of writing here at my residence.


My homepage; products to make money

Anonim mengatakan...

Great post. I was checking continuously this blog and I am impressed!

Extremely useful info particularly the closing phase :
) I deal with such info a lot. I was seeking this particular
info for a long time. Thanks and best of luck.

my page :: startup business ideas 2012

Anonim mengatakan...

This post is worth everyone's attention. Where can I find out more?

my site: search engin optimisation

Anonim mengatakan...

Thanks for a marvelous posting! I seriously enjoyed reading it, you could
be a great author.I will ensure that I bookmark your blog and will come back down
the road. I want to encourage yourself to continue your
great work, have a nice day!

Stop by my web page altersrückstellung private krankenversicherung

Anonim mengatakan...

Excellent blog you've got here.. It's difficult to find good quality writing like yours nowadays.
I really appreciate people like you! Take care!
!

Here is my webpage ... krankenversicherung selbständige vergleich

Anonim mengatakan...

I have been exploring for a little for any high-quality articles or blog posts in this kind of space .
Exploring in Yahoo I at last stumbled upon this site.
Studying this information So i'm satisfied to express that I've
a very excellent uncanny feeling I discovered exactly what I needed.
I most undoubtedly will make certain to do not
fail to remember this web site and provides it a glance regularly.


Feel free to surf to my webpage ... secured loans

Anonim mengatakan...

I am actually thankful to the owner of this web site who
has shared this fantastic article at at this time.

My web site :: Private Krankenversicherung Vergleichsrechner

Anonim mengatakan...

If you would like to grow your knowledge only keep visiting this web site and be updated
with the hottest news update posted here.

Check out my homepage :: unsecured consolidation loans

Anonim mengatakan...

Pretty part of content. I simply stumbled upon
your website and in accession capital to say that I acquire in fact loved account your blog posts.

Anyway I'll be subscribing in your feeds or even I success you get entry to persistently quickly.

Feel free to visit my web blog ... internet seo marketing

Anonim mengatakan...

It is truly a nice and useful piece of information.
I am glad that you just shared this helpful info with us. Please
stay us up to date like this. Thank you for sharing.


Also visit my webpage; online katalog mode

Anonim mengatakan...

Your style is really unique compared to other people I have read stuff from.
Thanks for posting when you have the opportunity, Guess I'll just bookmark this site.

Also visit my website :: cheap web hosting reviews

Anonim mengatakan...

I don't even know how I ended up here, but I thought this post was great. I do not know who you are but certainly you're going to a famous
blogger if you are not already ;) Cheers!

Take a look at my website :: onlinekredit

Anonim mengatakan...

Good day! Would you mind if I share your blog with my facebook group?
There's a lot of people that I think would really appreciate your content. Please let me know. Cheers

my webpage - Klicken Sie hier

Anonim mengatakan...

It is not my first time to go to see this site, i am visiting this web site dailly and get good information from here all the time.


Here is my blog :: kredit trotz schufa eintrag möglich

Anonim mengatakan...

I got this site from my buddy who told me on the topic of
this site and now this time I am visiting this web page and reading very informative posts at this
place.

My page; very bad credit loans

Anonim mengatakan...

Good day! I know this is kind of off topic but
I was wondering if you knew where I could get a captcha plugin for my comment form?
I'm using the same blog platform as yours and I'm having trouble finding one?
Thanks a lot!

my blog post; getting a home mortgage with bad credit

Anonim mengatakan...

Hello there! Would you mind if I share your blog with
my facebook group? There's a lot of people that I think would really appreciate your content. Please let me know. Cheers

Here is my homepage :: die private krankenversicherung

Anonim mengatakan...

Continue working, good job!

Also visit my blog post; web optimization company

Anonim mengatakan...

Excellent write-up, but to deal with that friend of Taiwan.
I Stumble UP your weblog, then we will determine that the
increase in site visitors within 24 hours of dedicated individuals.
Cheers

my blog: seo expert a.s.

Eddy Soesanto mengatakan...

Thank you for appreciation.
I just share what i have known to everyone.
ok, i will take a look your web.
Don't forget to visit my tiny blog.

Eddy Soesanto mengatakan...

to Anonim (anybody) who sent the comment on April 25,
Wow that's great!!!
Allrigt please promote my blog on your facebook page.
thank you soo much.

Anonim mengatakan...

Wow! What an concept! What a concept! Stunning .. amazing .
..

Look at my webpage ... how earn money online

Anonim mengatakan...

Super-Duper site! I am loving it!! Will come back again
- taking you feeds also, Thanks.

my homepage - all inclusive vacations with kids

Anonim mengatakan...

Your blog appears prestigious. Have an excellent day.


My webpage :: best hosting service

Anonim mengatakan...

I do not respond to messages, but on this case.
WoW! '

Feel free to visit my blog post ... einkommensgrenze private krankenversicherung ()

Anonim mengatakan...

My spouse and I absolutely love your blog and find most of your post's to be precisely what I'm looking for.
Does one offer guest writers to write content to suit your needs?
I wouldn't mind writing a post or elaborating on many of the subjects you write related to here. Again, awesome site!

My weblog; how to get A mortgage *icsci.it*

Anonim mengatakan...

Hey There. I found your blog using msn. This is a really well written
article. I'll be sure to bookmark it and return to read more of your useful information. Thanks for the post. I will definitely return.

Feel free to visit my blog post - how to buy a house **

Anonim mengatakan...

Hello would you mind sharing which blog platform you're working with? I'm
going to start my own blog in the near future but I'm having a hard time choosing between BlogEngine/Wordpress/B2evolution and Drupal. The reason I ask is because your design seems different then most blogs and I'm
looking for something unique. P.S Apologies for being
off-topic but I had to ask!

my webpage: home owner

Anonim mengatakan...

We're a group of volunteers and starting a new scheme in our community. Your site offered us with valuable info to work on. You have done an impressive job and our entire community will be thankful to you.

my web page; home owner :: ::

Anonim mengatakan...

Wow, superb blog layout! How long have you been blogging for?
you made blogging look easy. The overall look of your website is fantastic, as well as the content!


Here is my website - home mortgage tips

Anonim mengatakan...

Amazing blog! Is your theme custom made or did you download
it from somewhere? A design like yours with a few simple tweeks would really make
my blog shine. Please let me know where you got your theme.
Cheers

Also visit my web page how To get a mortgage

Anonim mengatakan...

Oh my goodness! Amazing article dude! Thank you, However
I am having troubles with your RSS. I don't understand the reason why I cannot subscribe to it. Is there anybody getting the same RSS issues? Anyone who knows the answer will you kindly respond? Thanks!!

Feel free to visit my webpage - home buying :: ::

Anonim mengatakan...

You might be an incredibly smart particular person! :
)

Also visit my weblog ... how can i find cheap car insurance ()

Anonim mengatakan...

I have been hunting about for the greatest website to receive a single.:)

Here is my blog :: Übersetzer Norwegisch Deutsch Wien

Anonim mengatakan...

really Nice exercise! I completely enjoyed your short article.
Please post far more frequently any time you have
time. Thanks.

Feel free to visit my weblog: profischnell.com - türkische Übersetzung

Anonim mengatakan...

Do you exercising in this industry? You seem to acknowledge
quite a bit regarding the study.

My web site: part time online home based jobs

Anonim mengatakan...

Wow, here is usually a wonderful diary.

Look into my web page - making money with affiliates

Anonim mengatakan...

I sincerely loved your post. Will link back from my web site.
Please location more frequently when you've got time.
Thanks!

Look at my page - top home based business opportunities

Anonim mengatakan...

whoah this blog is great i love studying your articles. Keep up the great paintings! You understand, lots of persons are searching around for this information, you could aid them greatly. Occudgeaffepe

Anonim mengatakan...

Hello there! I could have sworn I've been to this site before but
after checking through some of the post I realized it's new to me.
Anyways, I'm definitely delighted I found it and I'll be book-marking and checking back frequently!


Seht nach Moeglichkeit da: geburtstagssprueche 18 gute Geburtstagssprueche fuer die zukunft

Anonim mengatakan...

Hurrah, that's what I was seeking for, what a material!
present here at this web site, thanks admin of this website.


Have a look at my weblog :: affordable auto insurance

Anonim mengatakan...

Hey I am so grateful I found your weblog, I really found you by mistake, while I was researching
on Aol for something else, Nonetheless I am here now and would just like to say cheers for a incredible post and
a all round exciting blog (I also love the theme/design),
I don't have time to browse it all at the moment but I have saved it and
also added in your RSS feeds, so when I have time I will be back to
read much more, Please do keep up the fantastic work.

My homepage - basement renovation ideas ()

Anonim mengatakan...

It's really a nice and helpful piece of information. I am satisfied that you
just shared this helpful info with us. Please keep us informed like
this. Thank you for sharing.

Also visit my webpage - perumahan di semarang atas