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 answer:

S =  47 cm²

Step-by-step explanation:

$$\begin{gathered} a=16\text{cm} \\ b=4\text{cm} \\ {S}_0=a\cdot b=16\cdot 4=64{\text{cm}}^2 \\ x+y=a \\ {x}^2=y^2+b^2 \\ x+y=16 \\ {y}^2=x^2+4^2 \\ x=15/2=\frac{15}{2}=7.5\text{cm} \\ y=17/2=\frac{17}{2}=8.5\text{cm} \\ {S}_1=\frac{b\cdot x}{2}=\frac{4\cdot 7.5}{2}=15{\text{cm}}^2 \\ {S}_2=x\cdot b=7.5\cdot 4=30{\text{cm}}^2 \\ {S}_3=(y-x)\cdot b/2=(8.5-7.5)\cdot 4/2=2{\text{cm}}^2 \\ S=S_1+S_2+S_3=15+30+2=47{\text{cm}}^2 \end{gathered}$$

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