Question

A square has a boundary of 12 cm.
(a) From the corner of this square, a small square of side 1 cm is cut off. Will the boundary of B be less or more? Find its length.



(b) If you cut a 1 cm square to get shape C, what will be the length of the boundary of C?

Answer 1

(a)
Length of each side of square A = 3 cm
Number of sides of square A = 4
Length of the boundary of square A = 4 × 3 cm
= 12 cm
Now, a small square of side 1 cm is cut off from one corner of square A.
∴ Length of the boundary of B = 2 cm + 1 cm + 1 cm + 2 cm + 3 cm + 3 cm
= 12 cm
Thus, the length of the boundary of square B will remain the same as that of square A.

(b)
Length of the boundary of C = 1 cm + 1 cm + 1 cm + 1 cm + 1 cm + 3 cm + 3 cm + 3 cm
= 14 cm