Question 6 - Figure it out - Page 150-152 - Chapter 7 Class 8 - Area (Ganita Prakash II)

Transcript

Question 6 Divide a square into 4 parts by drawing two perpendicular lines inside the square as shown in the figure. Rearrange the pieces to get a larger square, with a hole inside. You can try this activity by constructing the square using cardboard, thick chart paper, or similar materials.Let’s do this activity When you divide a square using two perpendicular lines, you can always rearrange those 4 pieces to form a larger, tilted square with a hole in the center. The Math Behind It Let's use a square (Area ). We drew our perpendicular lines offset by units. The Pythagorean theorem tells us the cut length is . When rearranged, the long diagonal cuts form the outer boundary of a new square (Area ). Where does the extra area come from? The original rightangled corners are pushed to the center, perfectly forming a hole (Area )!