Question Video: Finding the Area of a Triangle by Multiplying an Algebraic Expression by a Monomial Mathematics

A triangle has a height of (2𝑥 + 1) and a base of 2𝑥. Find the area of the triangle in terms of 𝑥.

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Video Transcript

A triangle has a height of two 𝑥 plus one and a base of two 𝑥. Find the area of the triangle in terms of 𝑥.

Now, we can’t know exactly what this triangle looks like. But if you wanted to sketch a triangle, you could do that. We know that the base is two 𝑥 and the height is two 𝑥 plus one. Now, even if you didn’t sketch a triangle, the most important thing that we remember here is how we find the area of a triangle. The area of a triangle is equal to one-half times the height times the base. And that means we’ll take a height of two 𝑥 plus one, plug it into our formula, and a base of two 𝑥. And then, of course, we’ll need to bring down the one-half.

When you look at two 𝑥 plus one times two 𝑥, you might recognize that this is in the reverse order we usually see. When we’re multiplying a monomial by an algebraic expression, most often, you’ll list the monomial first because the monomial is what we distribute. We need to multiply two 𝑥 by two 𝑥 and by one. If you feel more comfortable doing it with the monomial first, you can rewrite it. Either way, we have to multiply two 𝑥 by two 𝑥 and two 𝑥 by one. Two 𝑥 times two 𝑥 equals four 𝑥 squared, and two 𝑥 times one is two 𝑥.

However, we can’t forget our one-half. We’ll have to do this distribution a second time. We’ll have to multiply one-half by four 𝑥 squared and by two 𝑥. Four times one-half equals two. So four 𝑥 squared times one-half is two 𝑥 squared. And two 𝑥 times one-half will be equal to 𝑥. So we can say the area of a triangle with these dimensions is equal to two 𝑥 squared plus 𝑥.

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