Chapter 10: Heron's Formula

Heron's Formula

The Formula

For triangle with sides aa, bb, cc:

Semi-perimeter: s=a+b+c2s = \frac{a + b + c}{2}

Area = s(s−a)(s−b)(s−c)\sqrt{s(s-a)(s-b)(s-c)}

Example

Triangle with sides 5, 6, 7:

s=5+6+72=9s = \frac{5 + 6 + 7}{2} = 9

Area = 9×4×3×2\sqrt{9 \times 4 \times 3 \times 2} = 216\sqrt{216} = 666\sqrt{6} sq units

Application: Quadrilateral Area

  1. Divide into triangles using diagonal
  2. Find area of each triangle using Heron's
  3. Add both areas