Octagon area

An irregular convex octagon is inscribed in the circle. Its four adjacent sides have a length of 3, and the remaining four adjacent sides have a size of 2. What is the area of a given octagon?

Final Answer:

S =  36.7696

Step-by-step explanation:

$$\begin{gathered} a=3 \\ b=2 \\ {v}_1=\sqrt{2}\cdot a=\sqrt{2}\cdot 3=3\sqrt{2}\doteq 4.2426 \\ {v}_2=\sqrt{2}\cdot b=\sqrt{2}\cdot 2=2\sqrt{2}\doteq 2.8284 \\ {S}_1=\frac{a\cdot v_1}{2}=\frac{3\cdot 4.2426}{2}\doteq 6.364 \\ {S}_2=\frac{b\cdot v_2}{2}=\frac{2\cdot 2.8284}{2}=2\sqrt{2}\doteq 2.8284 \\ S=4\cdot S_1+4\cdot S_2=4\cdot 6.364+4\cdot 2.8284=26\sqrt{2}=36.7696 \end{gathered}$$

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