7. Given a regular tetrahedron $P-ABC$ with the side length of the base being 6 and the side length of the lateral edges being $\sqrt{21}$. Then the radius of the inscribed sphere of the tetrahedron is $\qquad$.
7. 1.

Let $P O \perp$ plane $A B C$ at point $O$. Then $O$ is the center of the equilateral $\triangle A B C$. Connect $A O$ and extend it to intersect $B C$ at point $D$, and connect $P D$. Thus, $D$ is the midpoint of $B C$.
It is easy to find that $P D=2 \sqrt{3}, O D=\sqrt{3}, P O=3$.
Let the radius of the inscribed sphere of this tetrahedron be $r$. Then
$$
\begin{aligned}
r & =\frac{3 V_{\text {tetrahedron } P A B C}}{S_{\triangle A B C}+3 S_{\triangle P A B}} \\
& =\frac{3 \times \frac{\sqrt{3}}{4} \times 6^{2}}{\frac{\sqrt{3}}{4} \times 6^{2}+3 \times \frac{1}{2} \times 6 \times 2 \sqrt{3}}=1 .
\end{aligned}
$$