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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.
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
Let's take the example of 2\times2
3\times3, 4\times4,
, and
grids 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.
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.
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.
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.
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.
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