How Many Rectangles do a 2×2 Square Have

Introduction

As a learner, if you are facing a problem in calculating rectangles in n×n squares then here in this article you come to know about the method of calculating the question given to find the number of rectangles formed by a 2×2 grid of squares and also you have to know the properties of a rectangle. Here are all your queries solved. So you must read the article.

Rectangles in 2×2 square

As you can see the given below there is a square of a 2×2 grid.

And in the figure, you can see the first 2 upper squares make one rectangle the same as the lower one, and the same process with the left side squares and right side ones.

These all combine to make 4 rectangles. Here the 2×2 grid square is also considered a rectangle so it means the small square which is made under it is also considered a rectangle at the end you came to know that the total number of rectangles formed by a 2×2 grid square is 4+4+1=9

Tricks of pattern to know the rectangle in n×n grid of squares.

Let's take the example of 2\times2

3\times3, 4\times4, , andgrids of squares.

Here is the pattern you can see below:

2\times2\\

(1+2)^2 =9

3\times3\\

(1+2+3)^2=36

4\times4\\

=(1+2+3+4)^2=100

This is the pattern from which you can easily find out the number of rectangles in an n×n square grid.

About rectangle

As a rectangle is a quadrilateral with four right angles and all four angles formed by a rectangle are equal these are equilateral triangles which means each angle is 90°.

A rectangle is also called a crossed rectangle which means a self-intersecting quadrilateral that consists of two opposite sides of a rectangle along with two diagonals two opposite sides are always parallel.

Characteristics of a rectangle

• A convex quadrilateral is known as a rectangle. If it's having these kinds of characteristics.

• A parallelogram at least has one right angle.

• Diagonals have equal lengths of a parallelogram.

• In a parallelogram ABCD, DCA, and ABD are congruent.

• An equiangular quadrilateral

• A quadrilateral with four right angles.

Traditionally classification of a rectangle

A rectangle is termed a special case parallelogram in which each pair of adjacent sides is perpendicular. It is a special case of the trapezium in which both points of opposite sides are parallel and equal in length. A trapezium is a convex quadrilateral that has one pair or parallel opposite sides. The boundary of a convex quadrilateral does not cross itself.

Conclusion

In this article, you come to an end and see what are the things explained here in a simple and easy language which makes your doubts clear. These topics will help you in your upcoming time as it is based on the general properties of a figure as well the method or tricks used here also help you in doing these kinds of questions easily.