Trapezoid MO-5-Z8

ABCD is a trapezoid that lime segment CE is divided into a triangle and parallelogram, as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE, and the area of the triangle CDE is 3 cm².
Determine the area of the trapezoid ABCD.

Correct result:

S =  12 cm²

Solution:

$$\begin{gathered} \mathrm{\mid }EX\mathrm{\mid }=\mathrm{\mid }XB\mathrm{\mid } \\ S(CDE)=S(AED)=3 \\ S(FCD)=S(FDE)=3\mathrm{/}2=1.5 \\ S(EFX)=S(FCD)=1.5 \\ S(AEDC)=2\cdot 3=6 \\ S(XBCD)=S(AEDC)=2\cdot 3=6 \\ S=S(AEDC)+S(XBCD)-S(FCD)+S(EFX) \\ S=6+6-1.5+1.5=12{\text{cm}}^2 \end{gathered}$$

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Math student

The answer is 12 cm²

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