Triangle with two slopes and x-axis

Question

Triangle has:

Side 1 (p): x-2y+1=0

Side 2 (q): x+y-2=0

Side 3: x-axis

What is the area of this triangle?

I know that it has 2 equal sides but I have no idea how to solve this.

Answer 1

I guess you mean the area of the triangle. First find the two vertices on $x$-axis by substituting $y=0$ into (p) and (q), and you'll get $(-1,0),(2,0)$, the length of the side along the $x$-axis is $3$.

Now solve (p) and (q) to get the third vertex $(1,1)$. So the height corresponding to the side above is $|1|=1$.

Therefore the area is $A=\frac{1}{2}\cdot 3\cdot 1=\frac{3}{2}$.