Perpendicular sides

In the ABCDEFGHIJKL, the two adjacent sides are perpendicular to each other, and all sides except the AL and GF sides are identical. The AL and GF sides are twice as long as the other sides. The lines BG and EL intersect at point M. The quadrilateral ABMJ has an area of 1.8 cm². Find the area of the EFGM rectangle.

Final Answer:

S =  4.2 cm²

Step-by-step explanation:

$$\begin{gathered} S_1=1.8{\text{cm}}^2 \\ {S}_1=(1/2+1/4)S_2 \\ {S}_2=S_1/(\frac{1}{2}+\frac{1}{4})=1.8/(\frac{1}{2}+\frac{1}{4})=\frac{12}{5}=2.4{\text{cm}}^2 \\ a=\sqrt{S_2}=\sqrt{2.4}\doteq 1.5492\text{cm} \\ S=S_2\cdot (1+1/2+1/4)=2.4\cdot (1+1/2+1/4)=4.2{\text{cm}}^2 \end{gathered}$$

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