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Squares and Rectangles

Look at this image and identify what shapes these are.
You are right! These are the squares and rectangles.
Before discussing more about these shapes; let us see
how we can draw this image on a dot paper.

To draw a square and four rectangles on a dot paper,
proceed as follows:
Step 1: Draw a square on a dot paper with measurement
9 units × 9 units, where the space between two dots is
considered as 1 unit.
Step 2: Now, to place four rectangles symmetrical around the square, first we draw one rectangle,
which is 8 units by 3 units, 1 unit upward and 1 unit leftward to the square. And one rectangle,
which is 1 unit upward and 1 unit rightward to the square.

Step 3: Similarly, draw two rectangles below the square as we have drawn above.

Now we will study rectangles and squares in detail.

A Pinch of History

Historical Aspect of Geometry: Euclid is called the father of Geometry. He has written 13
volumes of book called ‘Elements’ which is one of the most beautiful and influential works of
science in the history of humankind. Its beauty lies in its logical development of geometry and
other branches of mathematics. It has influenced all branches of science but none so much as
mathematics and the exact sciences. The Elements consists of 465 propositions, divided into
13 “books” (an archaic word for “chapters”). The Elements were used as a textbook for more
than 1000 years in Western Europe, and they went through more than 2000 editions.

Rectangles
A B
Consider the rectangle ABCD.

The points A, B, C, and D are the corner points of the rectangle and the lines
AB, BC, CD, and DA are its sides. D C

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