Irregular pentagon

A rectangle-shaped, 16 x 4 cm strip of paper is folded lengthwise so that the lower right corner is applied to the upper left corner. What area does the pentagon have?

Correct result:

S =  47 cm2

Solution:

a=16 cm b=4 cm S0=a b=16 4=64 cm2  x+y=a x2=y2+b2  x+y=16 y2=x2+42=7.52+42=18  x=15/2=152=7.5 cm y=17/2=172=8.5 cm  S1=b x2=4 7.52=15 cm2 S2=x b=7.5 4=30 cm2 S3=(yx) b/2=(8.57.5) 4/2=2 cm2  S=S1+S2+S3=15+30+2=47 cm2



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