Construction of Square

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What are the Steps for Construction of a Square?

What is Square?

A square is a quadrilateral and a polygon with 4 vertices and 4 sides enclosing four angles, to note. 360 degrees is the sum of the interior angles. In general, a quadrilateral has sides of varying lengths and angles of different measurements. However, with some of their sides and angles being equal, triangles, rectangles, etc. are special kinds of quadrilaterals.


A square is a regular quadrilateral in geometry, which implies it has : 

  • Four equal sides.

  • Four equal angles (90-degree angles, or 100-gradian angles or right angles).

  • It can also be represented as a rectangle in which the length of two adjacent sides is equal.

  • A square with ABCD vertices will be denoted as □ABCD.

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Constructing a Square With a Compass

Square in construction is quite easy to draw as it requires only a few steps which are very easy to implement. While we focus on the square for construction, we have to take care of the following properties:

  • All the sides must be equal.

  • All the angles made by the sides of the square should be 90 degrees.

Therefore, the following are the steps for the construction of square:

  1. Draw a reference line AB of 6cm using a ruler.

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  1. Draw the 90 degree angle at A with the aid of the compass.

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  1. Draw the 90 degree angle at B with the aid of the compass.

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  1. Using an open compass 6 cm wide. Draw an arc with A as the centre; that cuts arms at a 90 degree angle. And mark the intersection point as C.

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  1. Using the ruler find length measure of AC. The AC length should be 6 cm.

  2. Using the compass again and take 6 cm width of the compass. With D as the middle, draw an arc that cuts arms at an angle of 90 degrees. And mark the junction point as D.

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  1. Using the ruler and the BD length measurement. The BD length should be 6 cm and we'll get:

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  1. Join CD.

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  1. Use the CD ruler and calculate its length. CD should be 6 cm in length and we get the corresponding square ABCD.

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Constructing a Square in a Circle

The steps to inscribe a square in a circle are:

  1. Draw a circle using your compass and mark the middle O.

  2. Draw a circular diameter using your ruler, marking the endpoints A and B.

  3. Build the perpendicular diameter bisector, AB.

  4. Label the points where the circle is intersected by the bisector as C and D.

  5. For the square to form, link points A to B to C to D.

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Solved Examples

1. Construct a square with a side of length 7cm.

Solution: 

  • Draw a reference line AB of 7 cm using a ruler.

  • Draw the 90 degree angle at A with the aid of the compass.

  • Draw the 90 degree angle at B with the aid of the compass.

  • Using an open compass 6 cm wide. Draw an arc with A as the centre; that cuts arms at a 90 degree angle. And mark the intersection point as C.

  • Using the ruler find length measure of AC. The AC length should be 6 cm.

  • Using the compass again and take 7 cm width of the compass. With D as the middle, draw an arc that cuts arms at an angle of 90 degrees. And mark the junction point as D.

  • Using the ruler and the BD length measurement. The BD length should be 6 cm and 

  • Join CD.

  • Use the CD ruler and calculate its length. The CD should be 7 cm in length and we get the corresponding square ABCD.

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2. Construct a circle with radius 5 cm and draw a square inside it.

Solution: 

  • Draw a circle with radius 5 cm using your compass and mark the middle O.

  • Draw a circular diameter using your ruler, marking the endpoints A and B.

  • Build the perpendicular diameter bisector, AB.

  • Label the points where the circle is intersected by the bisector as C and D.

  • For the square to form, link points A to B to C to D.

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Did You Know?

  1. A square is a regular quadrilateral since it has 4 sides of equal length.

  2. Often, a square is a rectangle with equal sides and a right-angled rhombus.

  3. A square's area equals the length of one side to the power of two (length squared).

FAQ (Frequently Asked Questions)

1. How do you Build a Rectangle and a Square?

Solution: Since we have learned how to construct a square, let us learn how the construction of a rectangle is different from the process of a square. To construct a rectangle, draw a  line AC of 6cm. Draw arcs, one on either side of AC, with centre A and radius over half of AC. Draw arcs that split the previous arcs P and Q with centre B and the same radius, respectively. Join PQ, which is perpendicular to BC and bisects half at BC. On both sides of AC, create an angle 45 at O that is above and below with respect to A and C.

OD is 3cm and OB is 3cm. Cut off. We'll get the length of DB as 6cm, then. Join in AD, DC, BC and BA. 

Thus, the rectangle needed is ABCD.

2. How is a Rectangle Different from a Square?

Solution: A rectangle and a square are similar in many ways as both of them are two-dimensional geometric figures, flat-shaped and closed, consisting of four sides and four angles. The inner angles are equal to 90 degrees, and the sides are parallel. A rectangle just like a square is a quadrilateral but as we know a square has all 4 sides equal, in case of a rectangle opposite sides are equal. A square diagonal is the perpendicular bisector of each other. A rectangular diagonal is not a perpendicular bisector of each other. Therefore, the formula to find the area and perimeter of both are also different.