Answer:
The measure of KN is 3 units.
Step-by-step explanation:
Given information: KLMN is a trapezoid , KF=1, MF || LK, altitude - h , Area of KLMF = Area of FMN
It means KLMF is a parallelogram with base KF=1 and height=h.
The area of a parallelogram is
[tex]A=base\times height[/tex]
The area of KLMF is
[tex]A_1=1\times h=h[/tex]
In triangle FMN, base FN and height h.
The area of a triangle is
[tex]A=\frac{1}{2}\times base\times height[/tex]
[tex]A_2=\frac{1}{2}\times FN\times h[/tex]
[tex]A_2=\frac{h}{2}(FN)[/tex]
It is given that
Area of KLMF = Area of FMN
[tex]h=\frac{h}{2}(FN)[/tex]
[tex]2h=h(FN)[/tex]
[tex]2=FN[/tex]
The length of FN is 2 units.
The length of KN is
[tex]KN=KF+FN=1+2=3[/tex]
Therefore the measure of KN is 3 units.
