Respectively 80982

The vertices of the square ABCD are joined by the broken line DEFGHB. The smaller angles at the vertices E, F, G, and H are right angles, and the line segments DE, EF, FG, GH, and HB measure 6 cm, 4 cm, 4 cm, 1 cm, and 2 cm, respectively.

Determine the area of square ABCD.

Correct answer:

S =  84.5 cm²

Step-by-step explanation:

$$\begin{gathered} DE=6\text{cm} \\ EF=4\text{cm} \\ FG=4\text{cm} \\ GH=1\text{cm} \\ HB=2\text{cm} \\ x=DE+FG+HB=6+4+2=12\text{cm} \\ y=EF+GH=4+1=5\text{cm} \\ u=\sqrt{x^2+y^2}=\sqrt{12^2+5^2}=13\text{cm} \\ u=\sqrt{2}\cdot a \\ a=u/\sqrt{2}=13/\sqrt{2}\doteq 9.1924\text{cm} \\ S=a^2=9.1924^2=84.5{\text{cm}}^2 \end{gathered}$$

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