Heron's Formula

Transcript

Heron's Formula Heron's Formula is way to find Area of Triangle when sides are given Area of Triangle = √(𝒔 (𝒔−𝒂)(𝒔−𝒃)(𝒔−𝒄)) Where s = Semi-perimeter = (𝒂 + 𝒃 + 𝒄)/𝟐 Let’s do an example Find Area of triangle with sides 9, 11 and 16 Given a = 9, b = 11, c = 16 Here, s = (𝒂 + 𝒃 + 𝒄)/𝟐 = (9 + 11 + 16)/2 = 18 Now , Area of Triangle = √(𝑠 (𝑠−𝑎)(𝑠−𝑏)(𝑠−𝑐)) = √(𝟏𝟖 (𝟏𝟖−𝟗) × (𝟏𝟖−𝟏𝟏) × (𝟏𝟖−𝟏𝟔)) = √(18 × 9 × 7 × 2) = √(36 × 9 × 7) = √36 × √9 ×√7 = 6 × 3 × √7 = 18√𝟕 square units