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Today we are going to look at Heron's formula. This is a formula to find the area of a triangle when you don't know the altitude but you do know the three sides. So here is our example. You have sides of 5, 6, and 7 in a triangle but you don't know the altitude and you don't have a way to. I'm going to share with you the formula, and then I'm going to run through an example of it. Heron's formula is when you have an unknown altitude but you know all the sides. The first step is to find S, S is the variable by adding all three sides up and divide by two. Then you take that S plug it into the formula as follows , the square root of S times S minus A ( which is the first side) times S minus B times S minus C ( which is the third side) It looks complicated but it is very easy. Multiple all this together and take the square root. That is how you find the area of a triangle. So let's work this out. The first step is to find S So I have to take A plus B plus C so I'm going to going to call 5 a 6 b and 7 is c after adding those up divide by two. When I add those up I get 18 and 18 divided by 2 is 9 so 9 is my magic s I then plug this S into the formula. You will have 9 times s minus A which is( 9 minus 5) times S minus B which is (9 minus 6 )times S minus C which is( 9 minus 7 )so I'm finding the difference between S for these three sides. This works out to be 9 times 4 times 3 times 2. Now when I multiply all of this out I get 216. I next have to take the square root of 216 So grab your calculator and the square root of 216 is 14,69 or you could round this to 14.7 square units. That is how you use Herron's formula to find the area of a triangle. Now I'm going to do a sing song thing to remember Herron's formula. It is the square root of s times s minus A times S minus B times S minus C equals the area of a triangle without an altitude. So sing along and you will have that down to. Hope this was helpful.
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