Triangle bounded by three lines

Find the triangle bounded by the three lines $y = x$, $y = -x + 4$, and $y = 0$ (the $x$-axis). Each vertex comes from solving two of the lines together. $y = x$ and $y = 0$ give $(0, 0)$; $y = -x + 4$ and $y = 0$ give $(4, 0)$; $y = x$ and $y = -x + 4$ give $x = 2, y = 2$, that is $(2, 2)$.

The large dots mark these three vertices. Taking the base along the $x$-axis from $(0, 0)$ to $(4, 0)$ gives length $4$, and the height is the $y$-coordinate $2$ of the apex $(2, 2)$, so the area is $\dfrac{1}{2} \times 4 \times 2 = 4$.