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.