Find the missing number in the following diagram:

31

The correct answer is Option (1) → 31

Look at the left diagram first:

• Top: 169 = 13²
• Bottom left: 49 = 7²
• Bottom right: 81 = 9²
• Center: 29

Now observe the pattern:

$\text{Center} = \sqrt{\text{Top}} + \sqrt{\text{Bottom Left}} + \sqrt{\text{Bottom Right}}$

$13 + 7 + 9 = 29$

Pattern confirmed.

Now apply the same rule to the right diagram:

• Top: 36 = 6²
• Bottom left: 121 = 11²
• Bottom right: 196 = 14²

$6 + 11 + 14 = 31$