# Heron's Formula

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. Heron’s formula is

S = is a variable and you find s using the formula

Let's work an example,
Find the area of a triangle with sides of  5, 6, and 7 units.
You have sides of 5, 6, and 7 in a triangle but you don’t know the altitude
Step 1. Find S  S is the variable by adding all three sides up and divide by two.
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.
Step 2. 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.  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 the answer is get 216.
Step 3.  Take the square root.
The square root of 216 is 14,69 or rounded 14.7
Please watch the video to see the problem worked out.
MooMooMath You Tube