MO Z9–I–2 - 2017

VO is a longer base in the VODY trapezoid, 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 answer:

S =  37.5 cm²

Step-by-step explanation:

$$\begin{gathered} S_1=13.5{\text{cm}}^2 \\ {k}_2=(2/3{)}^2=\frac{4}{9}\doteq 0.4444 \\ {S}_2=k_2\cdot S_1=0.4444\cdot 13.5=6{\text{cm}}^2 \\ {k}_3=(2+3)/3=\frac{5}{3}\doteq 1.6667 \\ {S}_3=k_3\cdot S_1-S_1=1.6667\cdot 13.5-13.5=9{\text{cm}}^2 \\ {k}_4=(2+3)/2=\frac{5}{2}=2.5 \\ {S}_4=k_4\cdot S_2-S_2=2.5\cdot 6-6=9{\text{cm}}^2 \\ S=S_1+S_2+S_3+S_4=13.5+6+9+9=\frac{75}{2}{\text{cm}}^2=37.5{\text{cm}}^2 \end{gathered}$$

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