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Area of Triangles - Problem 2

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

In this problem we are asked to find the area and we’re told that our units are in centimeters. Well since we have one pair of parallel sides, we have a trapezoid. So let’s start off by writing our area formula of a trapezoid.

That’s going to be the sum of the bases, base 1 plus base 2 times the corresponding height between those bases all divided by 2. Well the trick in this problem is realizing that we have more information than we need. So let’s start labeling what we know.

Base 1 has to be one of our parallel bases, so base 1 is going to be 12cm. Base 2 is the other base that’s parallel, so that’s going to be 16 and our last unknown is h, our height and that’s going to be the perpendicular segment in between your parallel bases, so that’s going to be 5 and these are units of centimeters.

So notice that I don’t need the 9 or the 7, those don’t help me at all. So now that I know my 3 unknowns I can solve for my area. So I’m just going to substitute in here area is equal to base 1 plus base 2 so that’s going to be 12 plus 16 times your height which is 5 all divided by 2. So area is equal to 12 plus 16 is 28 times 5 all divided by 2 and so there’s a couple of ways that we can do this. You could say that 2 goes into 28 14 times so we have 5 times 14 and 5 times 15 is 75 so if you take 5 away from that that’s going to be 70.

Now what are our units? When we’re talking about area we said that we have centimeters, so we’re going to have centimeters to the second power. Well the way that we’ll say that is 70 square centimeters. The key thing here was realizing that we had more information than we needed so we identified our three variables, substitute it and solved.

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