Question 1 - Think & Reflect (Page 142) - Squaring a Rectangle - Chapter 6 Class 9 - Measuring Space: Perimeter and Area (Ganita Manjar

Transcript

Question 1 - Think & Reflect (Page 142) What procedure would you use to square a given triangle? Here, the task is to construct a square whose area is equal to the area of some given triangle. Think carefully. How would you proceed? To square a triangle, you combine the knowledge from earlier in this chapter with Baudhāyana's method We cannot square a triangle directly using his method, so you must turn the triangle into a rectangle first. Let’s look at it step-by-step Step 2: Convert to a Rectangle. Cut horizontally at , split the top, and fold pieces down. Step 2 (Cont.): We have successfully transformed the triangle into a rectangle with length b and width ! Step 3: Square the Rectangle! Apply Baudhāyana's exact geometric steps (from Box 5 ) to this new rectangle. Finished! Because Square Rectangle, and Rectangle Triangle, this final Square has the exact area of the original Triangle!