Amen! Noah had already "found grace" (Genesis 6:8), was "a preacher of righteousness" (2 Peter 2:5), and "walked with God" BEFORE he built the ark. Building the ark was a DEMONSTRATION of his faith, not the origin of it.
Noah's obedience to God (works) had a part in his salvation along with his faith.
Faith is only mentioned two times in the entire Old Testament.
Salvation in the Old Testament was very much different than how it is today in the Church Age under the New Testament.
Now there are some similarities. We do see how Faith was demonstrated by the OT Patriarchs and Heros of the Faith (Heb. 11).
But one must keep in mind is that an OT Saint was not eternally secure like Christians are today. So an OT Saint many times had to secure his standing with God by doing the right kind of works. That's not heresy. That is Bible Doctrine.
By faith Abel offered a sacrifice (Heb. 11:4). Cain demonstrated an evil heart by his evil deeds, while Abel demonstrated a pious heart by his righteous deeds (1 John 3:12); and that Abel offered his sacrifice by faith and Cain did not.
Yep, Abel indeed offered a sacrifice (works), and he offered the right kind of sacrifice (right kind of works). Abel offered the firstlings and fat of his flocks (animal sacrifice) while Cain offered fruit of the ground. (No animal sacrifice: therefore no blood atonement)
While Cain also offered a sacrifice (works), but he offered the wrong kind of sacrifice. So did Cain exercise faith? Sure he did. But he did not do the right kind of works to accompany his faith.
You see; Abel had to do the work of killing the sacrifice and offering and then offer it unto God before he would be respected (Gen. 4:4). WORKS played a role along with faith therefore in his salvation.