Heron's formula
You can use Heron's formula to calculate the area of any triangle when you know the lengths of the three sides. If you call the lengths of the three sides a, b, and c, then here is the formula.
S is called the semiperimeter. The name makes sense because it is the perimeter divided by two.
A few examples showing how to use Heron's formula to calculate the area of triangles
Example #1:
Use Heron's formula to find the area of a triangle when a = 3 cm, b = 5 cm, and c = 4 cm
s = (3 + 5 + 4)/2 = 12/2 = 6
s − a = 6 − 3 = 3
s − b = 6 − 5 = 1
s − c = 6 − 4 = 2
s × (s − a) × (s − b) × (s − c) = 6 × 3 × 1 × 2 = 36
√(36) = 6
The area of this triangle is 6 cm
^{2}
Example #2:
Use Heron's formula to find the area of a triangle when a = 4 cm, b = 6 cm, and c = 8 cm
s = (4 + 6 + 8)/2 = 18/2 = 9
s − a = 9 − 4 = 5
s − b = 9 − 6 = 3
s − c = 9 − 8 = 1
s × (s − a) × (s − b) × (s − c) = 9 × 5 × 3 × 1 = 135
√(135) = 11.61
The area of this triangle is 11.61 cm
^{2}
Example #3:
Use Heron's formula to find the area of a triangle when a = 3/2 cm, b = 5/2 cm, and c = 2 cm
s = (3/2 + 5/2 + 2)/2 = (3/2 + 5/2 + 4/2)/2 = (12/2)/2 = 6/2 = 3
s − a = 3 − 3/2 = (6/2 − 3/2) = (6 − 3)/2 = 3/2
s − b = 3 − 5/2 = (6/2 − 5/2) = (6 − 5)/2 = 1/2
s − c = 3 − 2 = 1
s × (s − a) × (s − b) × (s − c) = 3 × 3/2 × 1/2 × 1 = 9/4
√(9/4) = 3/2
The area of this triangle is 1.5 cm
^{2}

Jan 20, 20 05:26 PM
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