Question: I am stumped on the following question

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> > PQRS is a parallelogram and ST=TR. What is the ratio of area of triangle QST to the area of parallelogram (Ans 1:4)
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![enter image description here](https://i.stack.imgur.com/o9JYN.png)

I need the height of the triangle, how would I get that? Any suggestions would be appreciated.

Answer: 
The complex projective line is the union of the two open subsets
$$
D\_i=\{[z\_0:z\_1]\text{ such that }z\_i\neq0\},\quad i=0, 1.
$$
Each of them is homeomorphic to $\Bbb C$, hence to the open unit disk.

Compacteness follows from the fact that it is homeomorphic to the sphere $S^2$. You can see this as a simple elaboration of the observation that
$$
\Bbb P^1(\Bbb C)=D\_0\cup[0:1].
$$
Yes.

In fact, the complex projective line "is" the [Riemann Sphere](http://en.wikipedia.org/wiki/Projective_line#Complex_projective_line%3a_the_Riemann_sphere).