Construct a square whose diagonal is $6 c m$ . Measure the side. Find also its area

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Solution

Given : $D i a g o n a l = 6 c m$ .
Steps for construction
Step $1$ : Draw the rough diagram and mark the given measures.
Step $2$ : Draw a line segment $A C = 6 c m$ .
Step $3$ : Construct a perpendicular bisector $\to X Y$ of $¯ ¯¯¯¯¯¯ ¯ A C$ .
Step $4$ : $\to X Y$ intersects $¯ ¯¯¯¯¯¯ ¯ A C$ at $O$ . We get $O C = A O = 3 c m$ .
Step $5$ : With $O$ as centre draw two arcs of radius $3 c m$ cutting the line $\to X Y$ at points $B$ and $D$ .
Step $6$ : Join $¯ ¯¯¯¯¯¯ ¯ A B, ¯ ¯¯¯¯¯¯ ¯ B C, ¯ ¯¯¯¯¯¯¯ ¯ C D$ and $¯ ¯¯¯¯¯¯¯ ¯ D A$ .
$A B C D$ is the required square

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