Heron’s Formula. Heron’s Formula is used to determine the area of any triangle when only the lengths of the three sides are known.

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Presentation transcript:

Heron’s Formula

Heron’s Formula is used to determine the area of any triangle when only the lengths of the three sides are known.

The ‘s’ represents the semi-perimeter.

The semi-perimeter is nothing more than half the perimeter.

Add the lengths of the three known sides together and then divide by two.

Next substitute the known values into Heron’s Formula then solve for the area.

A B C a b c Side a=5 Side b=8 Side c=7

First determine ‘s’, which is the semi-perimeter.

Now we know: Side a: = 5 Side b: = 8 Side c: = 7 Semi-perimeter: s = 10

Replace the letters in Heron’s Formula with their respective known values. (Substitute)

Another problem solved via trigonometry!

Try this one on your own! Side a = 5 Side b = 6 Side c = 7

Did you get Area = k = 14.7

Now for the solution of this problem.

First determine ‘s’, which is the semi-perimeter.

Now we know: Side a: = 5 Side b: = 6 Side c: = 7 Semi-perimeter: s = 9

This was created by Frank J. Antoniazzi Jr. on 15 April 2002