8. Construction of a square

A square can be constructed using a few known measurements.

 

The measurements are:

Let us construct a square with $5$ $cm$ as its side. Let us also find the area of the square obtained.

 

Step $1$: Draw a rough diagram for the measurements given.

 

 

Step $2$: Draw a line segment $AB$ of length $5$ $cm$.

 

 

Step $3$: With $A$ as centre, draw a perpendicular line.

 

 

Step $4$: With $A$ as centre and with $5$ $cm$ as radius, draw an arc on the perpendicular line. Mark the intersection as $D$.

 

 

Step $5$: With $D$ as centre and with $5$ $cm$ as radius, draw an arc. Similarly, with $B$ as centre and with $5$ $cm$ as radius, cut the existing arc. Mark the intersection as $C$.

 

 

Step $6$: Join $BC$ and $CD$ to form the desired square.

 

 

To find the area of the square:

 

$\text{Area of a square} = \text{Side} \times \text{Side}$

 

 

Step $1$: Draw a rough diagram with the measurements known.

 

 

Step $2$: Draw a line segment $AC$ of length $10$ $cm$.

 

 

Step $3$: Draw a perpendicular bisector to $AC$ such that the bisector intersects $AC$ at $O$.

 

 

Step $4$: With $O$ as centre and with $5$ $cm$ as radius, draw arcs on both sides of the perpendicular bisector. Mark the intersections as $B$ and $D$.

 

 

Step $5$: Join $AB$, $BC$, $CD$, and $AD$ to form the desired square.

 

 

To find the area of the square: