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

Result

S =  900

Solution:

p1=75 p1=2a+2 a/4 p1=2.5 a a=p1/2.5=75/2.5=30 S=a2=302=900p_{ 1 } = 75 \ \\ p_{ 1 } = 2a+2 \cdot \ a/4 \ \\ p_{ 1 } = 2.5 \ a \ \\ a = p_{ 1 }/2.5 = 75/2.5 = 30 \ \\ S = a^2 = 30^2 = 900



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