Triangle circle radius

Given is an isosceles triangle whose base is 8 cm, and the sides are 15 cm long. Calculate the area of the triangle and the radius of the inscribed and circumscribed circle.

Final Answer:

S =  57.8273 cm²
r =  3.0435 cm
R =  7.7818 cm

Step-by-step explanation:

$$\begin{gathered} a=8\text{cm} \\ b=15\text{cm} \\ {b}^2=h^2+(a/2{)}^2 \\ h=\sqrt{b^2-(a/2{)}^2}=\sqrt{15^2-(8/2{)}^2}=\sqrt{209}\text{cm}\doteq 14.4568\text{cm} \\ S=\frac{a\cdot h}{2}=\frac{8\cdot 14.4568}{2}=4\sqrt{209}=57.8273{\text{cm}}^2 \end{gathered}$$

$$\begin{gathered} s=(a+2\cdot b)/2=(8+2\cdot 15)/2=19\text{cm} \\ S=s\cdot r \\ r=S/s=57.8273/19=3.0435\text{cm} \end{gathered}$$

$$\begin{gathered} S=\frac{abc}{4R} \\ R=\frac{a\cdot b\cdot b}{4\cdot S}=\frac{8\cdot 15\cdot 15}{4\cdot 57.8273}=7.7818\text{cm} \end{gathered}$$

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