MO Z9–I–2 - 2017

In the VODY trapezoid, VO is a longer base and the diagonal intersection K divides the VD line in a 3:2 ratio. The area of the KOV triangle is 13.5 cm2. Find the area of the entire trapezoid.

Correct result:

S =  37.5 cm2

Solution:

S1=13.5 cm2 k2=(2/3)2=490.4444 S2=k2 S1=0.4444 13.5=6 cm2 k3=(2+3)/3=53=1231.6667 S3=k3 S1S1=1.6667 13.513.5=9 cm2 k4=(2+3)/2=52=212=2.5 S4=k4 S2S2=2.5 66=9 cm2 S=S1+S2+S3+S4=13.5+6+9+9=752=3712=752 cm2=37.5 cm2



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