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# herons formula

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```Heron’s Formula to find the Area of a Triangle
Reminder: If you know the base and height of a triangle: Area =
New for us: If you know the 3 side lengths of a triangle,
you can use Heron’s formula to find the area.
The area, A, of a triangle with sides measuring a, b, and c is:
A=
s (s  a )(s  b )(s  c ) ,
where s =
a b c
2
Example 1: Use Heron’s formula to find the area of the triangle.
First, we need to find s: s =
9m
5m
9  5  12
= 13
2
12m
Now, we can plug in to Heron’s Formula to find the Area:
A=
13(13  5)(13  9)(13  12)
=20.4m2
Example 2: You try! Find the area of a triangle with sides a = 9in b = 11in, and c = 13in.
(You should get 48.8 in2)
Example 3: You try! A farmer has a triangular field with sides of 200 feet, 350 feet, and 400
feet. He wants to apply fertilizer to the field. If one 35-pound bag of fertilizer covers 5,000
square feet, how many bags must he buy to cover the field? (you should get 7 bags)
Name _____________________________________ Date ____________ Per_________
Assignment: must complete at least 4 problems. Other 2 are Bonus.
Due at end of class
1. Use Heron’s formula to find the area to nearest tenth of a triangle with
sides 4m, 6m, and 8m.
2. Find b to nearest tenth:
9
b
17
10
3. A farmer has determined that a crop of strawberries yields a yearly profit of \$1.50 per
square yard. If strawberries are planted on a triangular piece of land whose sides are 50
yards, 75 yards, and 100 yards, how much profit, to the nearest dollar, would the farmer
expect to make from this piece of land during the next harvest?
4. A triangular plot of land has sides that measure 5 meters, 7 meters, and 10 meters.
What is the area of this plot of land, to the nearest tenth of a square meter?
5. A farmer has a triangular field with sides of 240 feet, 300 feet, and 360 feet. He wants to
apply fertilizer to the field. If one 40-pound bag of fertilizer covers 6,000 square feet, how
many bags must he buy to cover the field?
6. Find the area to nearest tenth of the triangle given a = 43ft., b = 32ft., c = 51ft.
```
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