Trapezoid MO-5-Z8

ABCD is a trapezoid that lime segment CE 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.

Result

S =  12 cm²

Solution:

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

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Math student

The answer is 12 cm²

3 years ago  Like

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