Right isosceles triangle

What can be the area of a right isosceles triangle with a side length of 8 cm?

Correct answer:

S₁ =  32 cm²
S₂ =  16 cm²

Step-by-step explanation:

$$\begin{gathered} a=8\text{ cm } \\ {S}_1={\displaystyle \frac{a\cdot a}{2}}={\displaystyle \frac{8\cdot 8}{2}}=32{\text{cm}}^2 \end{gathered}$$

$$\begin{gathered} c=8\text{ cm } \\ {c}^2=x^2+x^2 \\ x=c\mathrm{/}\sqrt{2}=8\mathrm{/}\sqrt{2}=4\sqrt{2}\text{ cm}\doteq 5.6569\text{ cm } \\ {S}_2={\displaystyle \frac{x\cdot x}{2}}={\displaystyle \frac{5.6569\cdot 5.6569}{2}}=16{\text{cm}}^2 \end{gathered}$$

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