Folded square

ABCD is a square. The square is folded on the midpoint of AB and A is folded onto the fold, creating a shaded region. The perimiter of the shaded figure is 75. Find the area of square ABCD

Correct result:

S =  900

Solution:

$$\begin{gathered} p_1=75 \\ {p}_1=2a+2\cdot a\mathrm{/}4 \\ {p}_1=2.5a \\ a=p_1\mathrm{/}2.5=75\mathrm{/}2.5=30 \\ S=a^2=30^2=900 \end{gathered}$$

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