3. Triangle $\mathrm{XYZ}$ is inside square KLMN shown below so that its vertices each lie on three different sides of the square. It is known that:
- The area of square KLMN is 1 .
- The vertices of the triangle divide three sides of the square up into these ratios:
$$
\begin{array}{ll}
\mathrm{KX}: \mathrm{XL} & =3: 2 \\
\mathrm{KY}: \mathrm{YN} & =4: 1 \\
\mathrm{NZ}: \mathrm{ZM} & =2: 3
\end{array}
$$

What is the area of the triangle XYZ? (Note that the sketch is not drawn to scale).
3. The length of each side is 1 .
$$
\begin{aligned}
\text { Area of grey triangle }= & \text { Area of square } \\
& -(\text { Area of two white triangles }+ \text { area of trapezium) } \\
= & 1-\left[1 / 2 * \frac{3}{5} * \frac{2}{5}+1 / 2 * \frac{4}{5} * \frac{1}{5}+1 / 2 *\left(\frac{3}{5}+\frac{2}{5}\right) * 1\right] \\
= & 1-\left[\frac{3}{25}+\frac{2}{25}+\frac{1}{2}\right] \\
= & \frac{3}{10} \text { units }^{2}
\end{aligned}
$$