Question

A small square of side 1 cm is cut off from each of its corners. Will the perimeter change?

Answer 1

Hint: Here, we will find the perimeter of the square before cutoff the square by using the given information and formula of the perimeter of the square. Then we will find the perimeter of the polygon after cutoff by adding the length of each side. We will then compare both the perimeters to find the change in the perimeter.

Complete step-by-step answer:
We are given a square with \[4\] small squares of 1 cm.
Now, we will find the perimeter of a square before cutoff.
Here, in the figure, one side has 2 small square in the figure of 1 cm and the length of the middle portion is of 2cm. This means the side of the bigger square is 4cm.
Now we will find the Perimeter of a square using the formula Perimeter of a square \[ = 4a\]. Therefore, we get
Perimeter of the square before cutoff the square \[ = 4\left( 4 \right){\rm{cm}}\]
Multiplying the terms, we get
\[ \Rightarrow \] Perimeter of the square before cutoff the square \[ = 16{\rm{cm}}\]
If a small square of side 1 cm is cut off from each of its corners, then the square changes its shape into a polygon.
We will find the perimeter of the polygon by adding all the sides of a polygon.
Perimeter of the polygon \[ = 1 + 1 + 2 + 1 + 1 + 2 + 1 + 1 + 2 + 1 + 1 + 2\]
\[ \Rightarrow \] Perimeter of the polygon \[ = 16\]
Thus the perimeter does not change.
Therefore, the perimeter will not change if a small square is cut off from each of its corners.

Note: We know that all the sides of a square are equal. A regular two dimensional shape has a formula to find their perimeters of the shape whereas the perimeter of the polygon is found by adding the sides of the polygon. A perimeter is defined as the path that is surrounding a two dimensional shape. We should know the property of two dimensional shapes to find the perimeter.