Question 1 - Page 153 - Area of Shaded Region - Chapter 6 Class 8 - We Distribute yet things Multiply (Ganita Prakash)

Transcript

Question 1 - Page 153 Find the area of the (interior) shaded region in the figure below. All four rectangles have the same dimensions.We do this by two methods Tadang’s Method Yusuf’s Method Let’s do it one by one Tadang’s Method Here, we have Big square of side (m + n) Four pink rectangles with sides m and n Thus, Area of interior shaded region = Area of big square – 4 × Area of pink rectangle = (𝒎+𝒏)^𝟐−𝟒 × (𝒎𝒏) = 𝑚^2+𝑛^2+2𝑚𝑛−4𝑚𝑛 = 𝑚^2+𝑛^2−2𝑚𝑛 = (𝒎−𝒏)^𝟐 square units Yusuf’s Method Yusuf finds side of the inner square Side of inner square = (𝒏−𝒎) Thus, Area of interior shaded region = Area of sinner square = (𝒏−𝒎)^𝟐 square units = (𝒎−𝒏)^𝟐 square units Note: Always (𝒏−𝒎)^𝟐=(𝒎−𝒏)^𝟐 Example: (5 – 2)2 = (2 – 5)2