Heron's Formula

Semi-perimeter

Meaning: Sem$i-p$erimeter is half the perimeter.

Definition: $s = (a + b + c) / 2$.

For sides 5, 6, 7, $s = (5 + 6 + 7) / 2 = 9$.

Heron's Formula

Meaning: The formula finds area using three sides.

Definition: Are$a = \sqrt{s(s-a}$($s-b$)($s-c$)).

Use the sem$i-p$erimeter and subtract each side from it.

Triangle Check

Meaning: The sides must form a valid triangle.

Definition: The sum of any two sides must be greater than the third side.

Sides 2, 3, and 8 cannot form a triangle because $2 + 3$ is not greater than 8.

• Check before calculating area.

Easy

Question: Find s for sides 6 cm, 8 cm, and 10 cm.

1. $s = (6 + 8 + 10) / 2$.
2. $s = 24 / 2 = 12$ cm.

Medium

Question: Find the area of a triangle with sides 3 cm, 4 cm, and 5 cm.

1. $s = (3 + 4 + 5) / 2 = 6$.
2. Are$a = \sqrt{6(6-3}$($6-4$)($6-5$)).
3. Are$a = \sqrt{6 x 3 x 2 x 1} = \sqrt{36} = 6$ c$m^{2}$.

Exam-level

Question: Can sides 4 cm, 5 cm, and 12 cm use Heron's formula?

1. Check triangle inequality.
2. $4 + 5 = 9$, which is not greater than 12.
3. These sides do not form a triangle.