Circumradius, you say?

We will prove that the area of a triangle can be given by the formula $A=\dfrac{abc}{4R}$ , where $a$ , $b$ , and $c$ are the corresponding sides of $\Delta ABC$ , and $R$ is the circumradius.

The area of a triangle is $A=\dfrac {1}{2} ab \sin C$ . $\sin C$ can be rewritten as $\dfrac {c}{2R}$ by Extended Sine Rule. Substituting, we get, $A=\dfrac {abc}{4R}$ . Thus proven.

Now, we have that the product of the sides of the triangle is equal to the triangle's area. Thus, we must have $4R=1$ , or $R=0.25$ . Thus, the circumradius must have a length of $0.25$ .

$R=\dfrac{abc}{4*area}=\dfrac{abc}{4*abc}=\frac 1 4=0.25.$