Circumference 7065

In an isosceles triangle, the length of the base is equal to 75% of the arm's length. Determine the area of the triangle if the circumference is 22 cm.

Correct answer:

S =  22.2486 cm²

Step-by-step explanation:

$$\begin{gathered} o=22\text{cm} \\ z=0.75\cdot r \\ o=2r+z \\ o=2r+0.75\cdot r \\ r=o/2.75=22/2.75=8\text{cm} \\ z=0.75\cdot r=0.75\cdot 8=6\text{cm} \\ h=\sqrt{r^2-(z/2{)}^2}=\sqrt{8^2-(6/2{)}^2}=\sqrt{55}\text{cm}\doteq 7.4162\text{cm} \\ S=\frac{z\cdot h}{2}=\frac{6\cdot 7.4162}{2}=3\sqrt{55}=22.2486{\text{cm}}^2 \end{gathered}$$

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