Question

Given: KLMN is a trapezoid, KF = 1, MF ║ LK , altitude −h. Area of KLMF = AFMN. Find: KN

Answer 1

it's 3 units due to the fact that KF is = to 1 and you need it to have the same area of the triangle. So I got 3

Answer 2

Answer:

The measure of KN is 3 units.

Step-by-step explanation:

Given information: KLMN is a trapezoid, KF = 1, MF ║ LK , altitude is h. Area of KLMF = Area of FMN.

The area of parallelogram is

$A=base \times height$

Area of parallelogram KLMF is

$A_1=KF \times h$

$A_1=1 \times h$

$A_1=h$

Area of a triangle is

$A=\frac{1}{2}\times base\times height$

Area of triangle FMN is

$A_2=\frac{1}{2}\times FN\times h$

$A_2=\frac{h(FN)}{2}$

It is given that Area of KLMF = Area of FMN.

$A_1=A_2$

$h=\frac{h(FN)}{2}$

$\frac{2h}{h}=FN$

$2=FN$

The length of FN is 2 units.

The length of KN is

$KN=KF+FN=1+2=3$

Therefore, the measure of KN is 3 units.