Isosceles 7566

A right isosceles triangle is inscribed in the circle with r = 8 cm. Find triangle area S. How much percent does the triangle occupy the area of ​​the circle?

Correct answer:

S =  64 cm²
p =  31.831 %

Step-by-step explanation:

$$\begin{gathered} r=8\text{cm} \\ S=\frac{2\cdot r\cdot r}{2}=\frac{2\cdot 8\cdot 8}{2}=64{\text{cm}}^2 \end{gathered}$$

$$\begin{gathered} S_1=\pi \cdot r^2=3.1416\cdot 8^2\doteq 201.0619{\text{cm}}^2 \\ p=100\cdot \frac{S}{S_1}=100\cdot \frac{64}{201.0619}=31.831\% \end{gathered}$$

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