Area of a Triangle - Heron's Formula The Area (A) of a triangle can be calculated using Heron's Formula, which is: A = (s(s - a)(s - b)(s - c)) / 4...
Area of a Triangle - Heron's Formula
The Area (A) of a triangle can be calculated using Heron's Formula, which is:
A = (s(s - a)(s - b)(s - c)) / 4
where:
s is the semiperimeter of the triangle, which is the sum of the lengths of the three sides.
a, b, c are the lengths of the three sides of the triangle.
Step 1: Find the Semiperimeter (s)
The semiperimeter of a triangle can be calculated by adding the lengths of all three sides. In other words, s = a + b + c.
Step 2: Identify the Side Lengths (a, b, c)
The three sides of a triangle are typically labeled as a, b, and c from the longest to the shortest side.
Step 3: Substitute the Side Lengths into Heron's Formula
Once you have the values of s, a, b, and c, you can substitute them into Heron's Formula to calculate the area of the triangle.
Example:
Let's say you have a triangle with the following measurements:
a = 6 cm
b = 7 cm
c = 8 cm
Using Heron's Formula, we can calculate the area of this triangle:
A = (s(s - a)(s - b)(s - c)) / 4 = (6(6 - 6)(6 - 7)(6 - 8)) / 4 = 21 cm²
Therefore, the area of the triangle is 21 square centimeters