The correct option is
A 13+23+33+43 Along the top row of the
4×4 square,
Total number of rectangle of size
1×1=4 Total number of rectangle of size
1×2=3 Total number of rectangle of size
1×3=2 Total number of rectangle of size
1×4=1 Total Number of rectangles in first row = 10
Now, along the first column,
Total number of rectangle of size
1×1=4 Total number of rectangle of size
1×2=3 Total number of rectangle of size
1×3=2 Total number of rectangle of size
1×4=1 Total Number of rectangles in first column = 10
Hence the total number of rectangle in
4×4 square grid
=10×10=102 Now
102=13+23+33+43 Therefore, total no of rectangles in
4×4 square grid
=13+23+33+43 Alternative Solution:
We know that
n×n square has
13+23+33+.....+n3 rectangles
Similarly,
4×4 square grid has
13+23+33+43 rectangles.