SOLUTION: A trapezium ABCD is split into four identical trapezia. Given that AB has length 6 cm, find the area of ABCD. If you would like to assist me with this question please ema

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A trapezium ABCD is split into four identical trapezia. Given that AB has length 6 cm, find the area of ABCD. If you would like to assist me with this question please ema      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1108613:
A trapezium ABCD is split into four identical trapezia.
Given that AB has length 6 cm, find the area of ABCD.
If you would like to assist me with this question please email me as it has an image of the trapezium abcd as a visual aid.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
We cannot email you because we do not know your email address.
However, If you enter a thank you note for this answer, the website will automatically email me telling me that a student is thanking me, and giving only me the email that you used to register.
If you prefer another email, then make the thank you note PRIVATE and include in the thank you note the email you want me to use.

NOTE: This system keeps your email address and mine private. We do not want to put them on display for everyone's eyes.

MY BET ABOUT THE IMAGE:

If that is how it is, we know some segment lengths:

We want to know height green%28h%29=CE and x=DE=AF .
The large trapezoid and the four smaller trapezoids are similar figures.
So, x%2F6=6%2F%286%2B2x%29 .
x%286%2B2x%29=6%2A6
2x%5E2%2B6x=36
2x%5E2%2B6x-36=0
x%5E2%2B3x-18=0
%28x%2B6%29%28x-3%29=0
x=3 because a negative length does not make sense.
Then,
green%28h%29=sqrt%286%5E2-3%5E2%29=sqrt%2836-9%29=sqrt%2827%29=3sqrt%283%29=about5.196
That makes the area of ABCD the same as the area of AGCE

%286%2B3%29%2A3sqrt%283%29=9%2A3sqrt%283%29=27sqrt%283%29
Although your teacher may prefer
BC%2B6 , AD=6%2B2x=6%2B2%2A3=6%2B6=12 , green%28h%29=3sqrt%283%29=about5.196
area%5BABCD%5D%22=%22%28BC%2BAD%29%2Agreen%28h%29%2F2%22=%22%2812%2B6%29%2A3sqrt%283%29%2F2%22=%229%2A3sqrt%283%29=27sqrt%283%29 .