[Maths Class Notes] on Construction of Square Pdf for Exam

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:

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

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

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

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

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8. Join CD.

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9. 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 inters
  ected 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).