Finding the Height of a Trapezoid

Video Transcript

"So how does one find the height of a trapezoid? Hi, I'm Jimmy Chang, I've been teaching college mathematics for 9 and a half years now and to find the height of a trapezoid it really depends on what kind of information that you are given. But one approach is using the formula for the area of a trapezoid because the area of a trapezoid uses the height. So if you take that formula and solve for height, you might be able to find the height of a trapezoid assuming you're given other bits of information. Now just to kind of review what a trapezoid looks like, you have a shape that's kind of like this, now the height of the trapezoid of course is from all the way up, all the way down as a straight line and remember a trapezoid has two bases, B1, the base on top and B2 which is the base on the bottom. Now the are of a trapezoid is of this formula, A is equal to 1/2 height times and then in parenthesis, B1 plus B1 so you have to add the two bases together and then multiply by half the height to get there. Now how do you find the height though? How do you solve for height and get height by itself? Just requires a little bit of algebra so here we go. First and foremost notice you already have a fraction so to make things easier, you can always clear the fraction. So go ahead and multiply both sides by the least common denominator which is 2, so we're going to multiply both sides by 2. So at the point the left side is 2A, the 2's here cancel so you're left with height times B1 plus B2. And then to get height completely by itself, you just divide both sides by the baggage if you will, the parenthesis B1 plus B2, B1 plus B2. So what will happen here is that the B1 plus B2's will cancel out on the right hand side and you'll have H and on the left you have 2A over B1 plus B2. And you now have height by itself and assuming if you have the area of the trapezoid that's provided and you know what the bases are, then you'll definitely be able to find the height of a trapezoid. So I'm Jimmy Chang and that's how you find the height of a trapezoid, keep on learning folks."