Question 4 - Figure it out - Page 169-170 - Chapter 7 Class 8 - Area (Ganita Prakash II)

Transcript

Question 4 [Śulba-Sūtras] Give a method to convert an isosceles trapezium to a rectangle using dissection.Method In an isosceles trapezium, the two slanted sides are equal. Drop a perpendicular line from one top vertex to the base. Cut off the resulting right-angled triangle. The Swap Slide that triangle to the other side of the trapezium. Because it’s isosceles, the triangle will fit perfectly against the other slanted side, turning the shape into a rectangle. Let’s visualize it Step 1: Start with an isosceles trapezium (where the two slanted sides are exactly equal).Step 2: Drop vertical lines from the top corners. This splits the shape into a central rectangle and two identical right-angled triangles.Step 3: Detach the right triangle. We need to move it to the other side to square off the shape.Step 4: Rotate the right triangle and slide its slanted edge perfectly against the left triangle's equal slanted edge.Result: The two side wings lock together to form a small rectangle, perfectly extending the central rectangle. The area is preserved!