Question

Construct a square whose area is 23.04 cm².

Answer 1

Given: Area of square = 23.04 cm².

Step-wise calculation:

1. Let side = a. Then a² = 23.04.

2. `a = sqrt(23.04)`

= `sqrt(2304/100)`

= `48/10`

= 4.8 cm

3. Construction (standard ruler-and-compass method when a side is given):

Draw segment AB = 4.8 cm.

At A construct a perpendicular to AB; on it mark point D so that AD = 4.8 cm.

At B construct a perpendicular to AB on the same side as AD; on it mark point C so that BC = 4.8 cm.

Join C to D. ABCD is the required square.

A square with area 23.04 cm² has side length 4.8 cm; construct it by drawing a side of 4.8 cm and erecting perpendiculars as described to complete the square.