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 Related: : Area of Triangle Home
 Area using Base and Height
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 Area of A triangle Calculator
The Formula
Heron's formula is named after Hero of Alexendria, a Greek Engineer and Mathematician in 10  70 AD. You can use this formula to find the area of a triangle using the 3 side lengths.
Therefore, you do not have to rely on the formula for area that uses base and height. The picture below illustrates the general fro mu la where S represents the semiperimeter of the triangle
Heron's Formula Applet
See applet on its own pageHeron's Formula Calculator
Side Lengths of TriangleExamples
Example 1
(Straight forward example)Use Heron's formula to find the area of triangle ABC, if side AB = 3 , BC = 2, CA =4
Step 1
S = (3+2+4) /2
S = 9/2 = 4.5
Round answer to nearest tenth
Since Heron's formula relates the side lengths, perimeter and area of a triangle, you might need to answer questions the like the following example.
Example 2
(a more challenging problem type)Given a triangle, with an area of 8.94 square units, a perimeter of 16 and side lengths AB = 3 and CA = 7, what is the length of side BC?
Step 1Calculate the semi perimeter, S
S = perimeter /2
S = 16/2 = 8
Substitute known values into the formula . Let x equal side length BC
Solve for x (square both sides and go from there)
Practice Problems
This problem is similar to example 1
Step 1Calculate the semi perimeter, S
S = (8 + 41 + 44) /2
S = 93/2 = 46.5
Substitute S into the formula. Round answer to nearest tenth
This problem is similar to example 1.
Step 1Calculate the semi perimeter, S
S = (7 + 6 + 8) /2
S = 21/2 = 10.5
Substitute S into the formula.
Round answer
to nearest tenth
This problem is similar to example 1
Step 1Calculate the semi perimeter, S
S = (11 + 12 + 5) /2
S = 28/2 = 14
Substitute S into the formula.
Round answer to nearest tenth
This problem is like example 2
Step 1Calculate the semi perimeter, S
S = perimeter /2
S = 32/2 = 16
Substitute known values into the formula . Let x equal side length CA
Solve for x (square both sides and go from there)
Picture of Triangle
Here is an accurate picture of a triangle with these side lengths, area and perimeter.
(Image was made using our triangle maker)This problem is like example 2.
Step 1Calculate the semi perimeter, S
S = perimeter /2
S = 26/2 = 13
Substitute known values into the formula . Let x equal side length CA
Solve for x (square both sides and go from there)
Picture of Triangle
Here is an accurate picture of a triangle with these side lengths, area and perimeter.
(Image was made using our triangle maker)