Divide a square into 4 parts by drawing two perpendicular lines inside the square as shown in the figure. Class 8

Divide a square into 4 parts by drawing two perpendicular lines inside the square as shown in the figure. Class 8

Question 1.

Divide a square into 4 parts by drawing two perpendicular lines inside the square as shown in the figure. Class 8

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.

Solution:

Note : Do as directed, rearranging as shown below :

Step 1 : Rotate each of the four pieces at 90° around at its centre and moving it outward.

Step 2 : When a bigger square is obtained, a small square shaped hole will appear in the centre. (See fig. alongside)

This technique is often referred to as Matsuyama’s Paradox.

Note : The area of the bigger square (including the hole) appears to greater than the original square, but in fact the side of the bigger square is slightly smaller than the original square.

Try to do it using thick chart paper in the Mathematics Laboratory.

Question 2.

In the given figure, which triangle has a greater area: ∆XDC or ∆YDC, if both the rectangles are identical? Class 8

Solution:

Both triangles have equal area, as both have area equal to half of identical rectangles.