Construct a square whose diagonal is 6cm. Measure the side. Find also its area.

To construct a square and solve the problem, follow these steps:

Understand the problem:

The square’s diagonal is given as 6 cm.
We need to construct the square, measure its side, and find its area.
Relationship between diagonal and side of a square:

In a square, the diagonal (d) and the side (s) are related by the Pythagoras theorem:
d = s√2
Rearranging to find the side, we get:
s = d / √2
Calculate the side:

Given d = 6 cm, substitute into the formula:
s = 6 / √2
To rationalize, multiply numerator and denominator by √2:
s = (6√2) / 2
s = 3√2 cm
Approximate the value of √2 = 1.414:
s ≈ 3 × 1.414 = 4.242 cm
Find the area:

The area (A) of a square is given by:
A = s²
Substitute s = 4.242 cm:
A ≈ (4.242)² ≈ 18 cm² (rounded to 2 decimal places).
Final Answer:
The side of the square is approximately 4.24 cm.
The area of the square is approximately 18 cm².