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In geometry, the area of a triangle is the number of square units that compose the triangle. It is the base times the height of a triangle: A = b h where "b" is the length of the base (or "base") and "h" is the height (or "altitude"). The area can also be calculated using the Heron's formula: A = 1/2 bh where "b" is the length of the base and "h" is the height. This formula only works for right triangles. The area is also equal to the average of the lengths of the bases times the height: A=b h = 1/ 2 ( b + h ).


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Video Transcript

at the area of a triangle. And I know you have learned how to do area of a triangle usually using a equals one half the base times height. However, in this lesson, we're gonna be looking at the area of a triangle using the trigonometry functions sine cosine tangent. We're gonna focus, really? On sign on this one, though. There's a couple of different ways you can find it. But when you have what we're gonna follow this rule for finding the area of a triangle. The area of a triangle is the product of the length of two sides is the product of I'm sorry. It's product of half the length of two sides and there sign of their included angle. So what we would do if we were finding area that we could do a different ways. It kind of depends on what information you're given. So to find the area you could if you're gonna use sign of a, you would use half of length be and late, see times sign of A. If you're gonna use sign of B, you're going to use half of a Tom C. Tom Sana be. And if you're going to use. See angle. See, it's gonna be half of a Tom's be sign of C. So depending on which angle you're given will depend on which side you're gonna want to use. But you're gonna follow the same process. So if I'm giving angle A I'm gonna use besides B and C to find my area. If I'm giving angle, see, I'm gonna use sides A and C. I'm sorry, A and B, I'm gonna use the opposite sides. And if I'm giving angle B, I'll use a and sit. So let's look at a couple of examples. Let's start with this one where we have a triangle where Ace side length of a s, five side length of CS six and angle B is 112 degrees. Well, in this one, I'm given Angle Bay. So this means that I'm going to use Side A and Side B course. I'm giving those sides so I can find the area. So to use an angle, a I mean angle be your area would be one half of a Tom's See son, Be so for this one, the substitute her numbers in place of our angles and sides. So we'd have half of a We've got five, and for see we have six and sign of 112 degrees. Well, we can go ahead and multiply one half times five times six is 30 Tom sign of 112 degrees and half of 30th 15. So we're really finding 15 times. Sign off 112 degrees and you'll definitely need to use your calculator on this one. So if I'm going to approximate, I'm gonna go ahead for this purpose. I'm going around it right now to 0.92 seven and 15 times. 0.9 to 7 is approximately 13.9 and we're going around these to the nearest 10th. So in the area of my triangle is approximately 13.9 units squared. So let's look at another one. This one. They didn't give us the actual triangle assed faras a picture, but they did give us our information. They told us that angle A is 31 degrees. Side B is 18 and side see is 22. This is all the information we need to find the area of this triangle. Since we're given angle A, we're gonna be used. Binding Sign of a. So that means that our area, we're going to use the formula one half of be Tom C son of angle A. So in this case, that's gonna be half of 18 times 22 sign of 31 18 times 22 is 396 and half of that is 198. So when around that I would have 198 and then sign a 31 I'm gonna have approximately 0.515 And that's going to give me an approximate area of 101 point. Not so All you're gonna do to kind of review is your whatever angle you're given, you're gonna use the two opposite sides because those were going to be the adjacent sides to that angle. You're gonna use those two leaks to find the area of the triangle