# MO Z8–I–6 2018

In the KLMN trapeze, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line.

Result

x =  28 cm

#### Solution:

$k=40 \ \text{cm} \ \\ m=16 \ \text{cm} \ \\ \ \\ S=\dfrac{ k+m }{ 2 } \cdot \ h \ \\ \ \\ S_{1}=\dfrac{ x \cdot \ h }{ 2 } \ \\ S_{1}=\dfrac{ S }{ 2 } \ \\ \dfrac{ x \cdot \ h }{ 2 }=\dfrac{ k+m }{ 4 } \cdot \ h \ \\ 2 \cdot \ x \cdot \ h=(k+m) \cdot \ h \ \\ x=(k+m)/2=(40+16)/2=28 \ \text{cm}$

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