How many? What? In this area of study, you ask these questions a lot. This area of study is geometry, because you have to ask how many sides and how much the area is or something (can you tell I don't remember any maths?).

The 学 is read correctly, in terms of what you learned. The 幾 and 何 is weird, though. Just think how when you're asking a question in Japanese, you end the sentence with か. So, it's like, "何か????" and that's why it becomes か. Then, for 幾 think about how the key (き) to answering geometry questions correctly is figuring out "how many" sides something has. So, "do you have the keyか?"