KLMN trapezoid

The KLMN trapezoid has bases KL 40cm and MN 16cm. On the KL base is point P. The segment NP divides the trapezoid into units with the same area. What is the distance of point P from point K?

Result

x =  28 cm

Solution:

k=40 cm m=16 cm  S=k+m2h S1=xh2 S2=S−S1 S1=S2  S1=S−S1 2S1=S  2⋅ xh2=k+m2h 2⋅ x2=k+m2 x=k+m2=40+162=28 cmk=40 \ \text{cm} \ \\ m=16 \ \text{cm} \ \\ \ \\ S=\dfrac{ k+m }{ 2 } h \ \\ S_{1}=\dfrac{ xh }{ 2 } \ \\ S_{2}=S-S_{1} \ \\ S_{1}=S_{2} \ \\ \ \\ S_{1}=S-S_{1} \ \\ 2S_{1}=S \ \\ \ \\ 2 \cdot \ \dfrac{ xh }{ 2 }=\dfrac{ k+m }{ 2 } h \ \\ 2 \cdot \ \dfrac{ x }{ 2 }=\dfrac{ k+m }{ 2 } \ \\ x=\dfrac{ k+m }{ 2 }=\dfrac{ 40+16 }{ 2 }=28 \ \text{cm}

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