Heron's Formula (NCERT Ch. 10)

• Compute semi-perimeter s = (a + b + c)/2.
• Apply Heron's formula Area = √(s(s−a)(s−b)(s−c)).
• Find areas of triangles when height is unknown but three sides known.
• Use in composite figures split into triangles.
• Check triangle inequality before applying formula.

1. Semi-perimeter s = (a+b+c)/2.
2. Heron's formula — Area = √(s(s−a)(s−b)(s−c)).
3. Works for any triangle with known three sides.
4. Units — Area in square units (m², cm²).
5. Triangle inequality — a+b > c, etc., must hold.
6. Example — sides 3, 4, 5 → s = 6 → area = √(6·3·2·1) = √36 = 6.
7. Applications — Land plots, irregular triangular regions.
8. NCERT Ex. 12.2 — numerical practice.

Find area of triangle with sides 5 cm, 6 cm, 7 cm.

s = (5+6+7)/2 = 9
Area = √(9·4·3·2) = √216 = 6√6 cm² ≈ 14.7 cm²

• Skipping given-to-prove structure in geometry proofs.
• Using wrong congruence criterion (SSA is not valid).
• Forgetting units in length/angle statements.

• State one NCERT result from Heron's Formula.
• Draw a neat diagram for a typical Heron's Formula problem.

Open the Practice tab for graded questions on Heron's Formula (NCERT Ch. 10).