Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 252 cm.

Correct result:

S =  2723.9 cm²

Solution:

$$\begin{gathered} p=2a+b \\ \sin \gamma \mathrm{/}2={\displaystyle \frac{b\mathrm{/}2}{a}} \\ b=2a\sin \gamma \mathrm{/}2=2a\sin 45^{\circ } \\ p=2a+b=2a+2a\sin 45^{\circ }=2a(1+\sin 45^{\circ }) \\ a={\displaystyle \frac{p}{2\cdot (1+\sin 45^{\circ })}}=73.809 \\ S={\displaystyle \frac{1}{2}}{a}^2={\displaystyle \frac{1}{2}}73.809^2=2723.9{\text{cm}}^2 \end{gathered}$$

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