$What\ is\ the\ area\ of\ the\ \ region\ included\ by\ the\ ellipse\ 4x^2+9y^2=36?$

To find the area of the region enclosed by the ellipse $4 x^{2}+9 y^{2}=36$, we start by identifying the standard form of the ellipse equation:

$\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$

Here, $a^{2}=9$ and $b^{2}=4$, where $a$ is the semi-major axis and $b$ is the semi-minor axis of the ellipse.

The formula for the area $A$ of an ellipse is given by

$A=\pi \times a \times b$

Substituting the values of $a$ and $b$ :

$\begin{array}{l} A=\pi \times \sqrt{9} \times \sqrt{4} \\ A=\pi \times 3 \times 2 \\ A=6 \pi \end{array}$

Therefore, the area of the region included by the ellipse $4 x^{2}+9 y^{2}=36$ is $6 \pi$.