Height
You've seen the word 高い from a couple levels ago. This word is related to that. It's like 大きい versus 大きさ, where one describes the other. In this case, the 高さ is the height of something (while 高い is tall). This word isn't "price" though. For that you'd ask いくらですか？ (how much is it?).
たかさ
Use the reading of 高い (たかい) to help you to learn and remember the reading for this one. They are the same with just the hiragana at the end different.
あいつのテンションの高さはやばいよな。
His excitement levels are dangerously high, right?
トーフグのサボテンは、1.5メートルの高さにまでせい長しました。
Tofugu's cactus has grown to a height of 1.5 meters.
「この建物の高さについてどう思いますか？少し高すぎますかねえ？」「申し訳ありませんが、分かりません。私には難しすぎます。」
"What do you think about the height of this building? Is it too high?" "Sorry, but I don’t know. It’s over my head."