Question

Construct a square, each of whose sides measures 5.5 cm.

Answer 1

Hint: Assume ABCD as the name of the square. Consider AB as the base whose length is 5.5 cm. Use the properties of squares that all the sides are of equal length and each angle equals 90 degrees, draw the square with the help of a ruler and compass.

Complete step-by-step solution:
Here, we are asked to construct a square. The side of the square is given as 5.5 cm.
Now, we know that a square is a quadrilateral having several properties listed below,

(i) All the sides of a square are equal in length.
(ii) Each angle measures 90 degrees.
(iii) Diagonals AC and BD of a square bisect each other at 90 degrees.
Now let us draw a square ABCD with each side measuring 5.5 cm. Follow the steps for construction.
Step 1: Draw a line segment AB of length 5.5 cm, considering it as a base. Use a ruler to draw the length.

Step 2: Construct perpendicular lines at points A and B with the help of a compass. To do this, place the compass at point A, draw an arc and bisect the angle of ${{180}^{\circ }}$. Do the same for point B. Extend these perpendicular lines.

Step 3: Now, cut a length of 5.5 cm from point A on its perpendicular and mark it as D. Similarly, cut a length of 5.5 cm from point B on its perpendicular and mark it as C.

Step 4: Join C and D, to form a line segment CD, with the help of a ruler to form the square ABCD.

Hence, our construction is complete.

Note: One must remember the properties of basic quadrilaterals like parallelogram, square, rectangle, rhombus, etc. as these are common shapes whose constructions are asked. In the above question, you must remember all the properties of squares to construct it. Here, it is not said that we have to use a compass, so you may use a protractor for the construction of 90 degrees. However, you must know how to construct angles of ${{30}^{\circ }},{{45}^{\circ }},{{60}^{\circ }},{{90}^{\circ }},{{120}^{\circ }}$ because sometimes it is not valid to use a protractor for the construction of these angles.