Right-angled 66344

From a square with a side of 4 cm, we cut four right-angled isosceles triangles with right angles at the square's vertices and with an overlap of √2 cm. We get an octagon. Calculate its perimeter if the area of ​​the octagon is 14 cm².

Correct answer:

o =  13.6569 cm

Step-by-step explanation:

$$\begin{gathered} a=4\text{cm} \\ c=\sqrt{2}=\sqrt{2}\text{cm}\doteq 1.4142\text{cm} \\ {c}^2=b^2+b^2 \\ b=c/\sqrt{2}=1.4142/\sqrt{2}=1\text{cm} \\ z=a-2\cdot b=4-2\cdot 1=2\text{cm} \\ o=4\cdot c+4\cdot z=4\cdot 1.4142+4\cdot 2\doteq 13.6569\text{cm} \\ \text{ Verifying Solution: } \\ {S}_1=a^2=4^2=16{\text{cm}}^2 \\ {S}_2=4\cdot \frac{b\cdot b}{2}=4\cdot \frac{1\cdot 1}{2}=2{\text{cm}}^2 \\ {S}_3=S_1-S_2=16-2=14{\text{cm}}^2 \end{gathered}$$

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