# Find the lengths of the parallel sides of a trapezium (US: trapezoid)

by Oshi
(Dubai)

##### Question
ABCD is a trapezium (US: trapezoid) of area 91cm2. CD is parallel to AB and CD is longer than AB by 8cm. if the distance between AB and CD is 7cm, find the lengths of AB and CD.
STEP 1:    We know that, the area is 91cm2 and CD is longer than AB. If we let AB be x, CD is will be x+8. Hence, we will have:

STEP 2: Now, since the distance between AB and CD is 7cm, the height of the trapezium is 7cm. Hence:

STEP 3:    To find the lengths of AB and CD, we need to find x. To do so, we start with the formula for the area of a trapezium:

Where a and b are the parallel sides of the trapezium and h is its height.

STEP 4:    So, to find x, we substitute a with x,b with x+8, h with 7 and A with 91. This gives:
STEP 5:    Now, we simplify the equation:
STEP 6:    Notice that, to find x, we need to remove 7. We can do so by dividing both sides of the equation with 7.

STEP 7:    Now, we can find x by adding -4 to both sides of the equation.

STEP 8:   With x=9, we can easily find the lengths of AB and CD:

### Comments for Find the lengths of the parallel sides of a trapezium (US: trapezoid)

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 Nov 28, 2022 Rating ;) NEW by: Anonymous this issssss sooooo helpful maybe later i can come back on....

 May 30, 2021 Rating SHIT SHIT NEW by: HELLO YOUR WEBSITE IS SHIT

 Jul 21, 2020 Rating but why NEW by: miss kentol lover i wanna noe how you get the opposite sides

 May 03, 2020 Rating Did not help me by: Anonymous Useless! I asked about the side when not given the area. Anyone can do it if given area

 Apr 19, 2020 Rating Shit by: PP It didn't help me at all, your website is shit

 Jan 08, 2019 Rating Nice by: Phenomenal How can I find area of a trapezium when given height and 1 parallel side ?

 Mar 04, 2018 Rating area? by: Anonymous what if the area is not given

 Feb 26, 2017 Rating Doubt by: Ayush In step 5 how you divided 7/2 with 2x and 8 there was only one 2 then how you divided 8 by it.

 Jul 18, 2016 Rating thanks by: rachel thank u!!!!!!!!!

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 Sep 02, 2015 Rating Thanks by: Anonymous Thank you!!! Your teaching had allowed me to gain a better understanding on solving math questions related to trapeziums.

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 Jan 17, 2011 Rating Thank u!!!! by: Anonymous Thanks dude u saved me from my math teacher. I lost my book & I needed to give the work tomorrow. I solved the question with ur help. You r a saviour for me today. You made my day. Thanks a lot!!!!!!!!!!!!!!

 Feb 25, 2010 Rating trapezium by: oshi thankyou oshi

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