Question 1 - Think & Reflect (Page 133) - Area of a Triangle - Chapter 6 Class 9 - Measuring Space: Perimeter and Area (Ganita Manjar

Transcript

Question 1 - Think & Reflect (Page 133) Since ΔABD and ΔACD have equal area, you may wonder — Can we divide ΔABD using straight cuts into two or more pieces that we can then rearrange to exactly cover ΔACD? What do you think? Is it possible? Yes, it is absolutely possible To do this for any generic triangle, the least number of pieces required is 3 pieces (which requires 2 straight cuts). You make one cut perfectly parallel to the base exactly halfway up the height, and a second vertical cut on the top piece, then rotate the pieces to form the new shape. Let’s visualise it Step 1 - Consider ∆ ABC with median AD Step 2 – Cut ∆ ABD halfway up the height horizontally Step 3 - Second cut: Make a vertical cut on the top piece of ΔABD. Step 4 - Rearrange: Rotate the two top pieces down to form a solid Rectangle! Step 5 – Slide: We slide this rectangle over Step 6 - The Shape Gap: The rectangle has an 'extra' piece sticking out (red), and ΔACD has 'missing' gaps (green). Mathematically, these red and green areas are exactly equal Step 7 – The Final Cover: We make a final cut along the diagonal of the rectangle's extra pieces. Watch as we rotate and slide these red pieces to perfectly fill the green gaps! ΔACD is now perfectly covered!