Question

Given: KLMN is a trapezoid, KF=10
MF parallel to LK, Area of KLMF = Area of FMN

Find: KN

Answer 1

@ganeshie8 @ghazi

Answer 2

Call the height of the trapezoid h, and then give each area in terms of h. Then you should be able to cancel out the h's and get FN in terms of KF, and hence 10. Does that help?

Answer 3

I dont get what you mean by hence 10

Answer 4

KF is 10, you're told that, so you can replace KF with 10, at the beginning or at the end! I can go through the equations if you want!

Answer 5

Yes please can you go through the equations

Answer 6

Ok, so h is the height, perpendicular to KF, of the trapezoid. And we know that the area of KLMF= the area of FMN. So, for FMN, the area is 1/2hFN, as the area of a triangle is 1/2 base x height.
The area of KLMF is just base x vertical height, so is 10 (KF) x h.
So,
\[\frac{ 1 }{ 2 }hFN=10h\]
Divide both sides by h, then times both sides by 2 and you get FN = 20.
So KN, is just KF + KN, which is 30!
Does that make sense?

Answer 7

yep

Answer 8

Awesome! :)