Example 6 - Chapter 6 Class 9 - Measuring Space: Perimeter and Area (Ganita Manjar

Transcript

Example 6 Verify Brahmagupta’s formula for the case of a rectangle. All rectangles are cyclic, so Brahmagupta’s formula should apply. Let’s consider a rectangle with Length a & Width b Thus, Sides of rectangle are a, b, a, b Using Brahmagupta’s formula So, a = a, b = b, c = a, d = b Here, s = (𝒂 + 𝒃 + 𝒂 + 𝒃)/𝟐 = (2𝑎 + 2𝑏)/2 = a + b Now , Area of 4-gon = √((𝑠−𝑎)(𝑠−𝑏)(𝑠−𝑐)(𝑠−𝑑)) = √((𝑎+𝑏−𝑎)(𝑎+𝑏−𝑏)(𝑎+𝑏−𝑎)(𝑎+𝑏−𝑏)) = √(𝒃 × 𝒂 × 𝒃 × 𝒂) = √(𝑎^2 × 𝑏^2 ) = 𝒂 × 𝒃 Thus, it matches Area of rectangle = Length × Breadth