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Number of Rectangles in Grid Calculator

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Geometric Combinatorics

✖Number of Horizontal Lines is the total count of given straight lines which are horizontally oriented on a plane.ⓘ Number of Horizontal Lines [N_{Horizontal Lines}]			+10% -10%
✖Number of Vertical Lines is the total count of given straight lines which are vertically oriented on a plane.ⓘ Number of Vertical Lines [N_{Vertical Lines}]			+10% -10%

✖Number of Rectangles is the total count of rectangles that can be formed by using a given set of horizontal and vertical lines from a plane.ⓘ Number of Rectangles in Grid [N_Rectangles]

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Number of Rectangles in Grid Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Rectangles = C(Number of Horizontal Lines+1,2)*C(Number of Vertical Lines+1,2)
N_Rectangles = C(N_{Horizontal Lines}+1,2)*C(N_{Vertical Lines}+1,2)
This formula uses 1 Functions, 3 Variables

Functions Used

C - In combinatorics, the binomial coefficient is a way to represent the number of ways to choose a subset of objects from a larger set. It is also known as the "n choose k" tool., C(n,k)

Variables Used

Number of Rectangles - Number of Rectangles is the total count of rectangles that can be formed by using a given set of horizontal and vertical lines from a plane.
Number of Horizontal Lines - Number of Horizontal Lines is the total count of given straight lines which are horizontally oriented on a plane.
Number of Vertical Lines - Number of Vertical Lines is the total count of given straight lines which are vertically oriented on a plane.

STEP 1: Convert Input(s) to Base Unit

Number of Horizontal Lines: 10 --> No Conversion Required
Number of Vertical Lines: 9 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_Rectangles = C(N_{Horizontal Lines}+1,2)*C(N_{Vertical Lines}+1,2) --> C(10+1,2)*C(9+1,2)

Evaluating ... ...

N_Rectangles = 2475

STEP 3: Convert Result to Output's Unit

2475 --> No Conversion Required

FINAL ANSWER

2475 <-- Number of Rectangles

(Calculation completed in 00.004 seconds)

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Created by Pramod Singh

Indian Institute of Technology (IIT), Guwahati

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< Geometric Combinatorics Calculators

Number of Rectangles in Grid

LaTeX Go Number of Rectangles = C(Number of Horizontal Lines+1,2)*C(Number of Vertical Lines+1,2)

Number of Rectangles formed by Number of Horizontal and Vertical Lines

LaTeX Go Number of Rectangles = C(Number of Horizontal Lines,2)*C(Number of Vertical Lines,2)

Number of Triangles formed by joining N Non-Collinear Points

LaTeX Go Number of Triangles = C(Value of N,3)

Number of Chords formed by joining N Points on Circle

LaTeX Go Number of Chords = C(Value of N,2)

Number of Rectangles in Grid Formula

LaTeX Go

Number of Rectangles = C(Number of Horizontal Lines+1,2)*C(Number of Vertical Lines+1,2)
N_Rectangles = C(N_{Horizontal Lines}+1,2)*C(N_{Vertical Lines}+1,2)

What are Combinations?

In combinatorics, Combinations refer to the different ways of selecting a subset of items from a larger set without regard to the order of selection. Combinations are used to count the number of possible outcomes when the order of selection does not matter. For example, if you have a set of three elements {A, B, C}, the Combinations of size 2 would be {AB, AC, BC}. In this case, the order of the items within each combination does not matter, so {AB} and {BA} are considered the same combination.

The number of Combinations of selecting "k" items from a set of "n" items is denoted as C(n, k). It is calculated using the binomial coefficient formula: C(n, k) = n! / (k! * (n - k)!)

Combinations have various applications in mathematics, probability theory, statistics, and other fields.

What is a Rectangle?

A Rectangle is a geometric shape that has four sides and four right angles. It is a type of parallelogram, which means that opposite sides are parallel and equal in length. The Length of a Rectangle is the distance along its longer side, and the Width of a Rectangle is the distance along its shorter side. The Area of a Rectangle is equal to its length multiplied by its width. The Diagonals of a Rectangle are also important geometric features, and they intersect at the center of the Rectangle. The Diagonals of a Rectangle are always equal in length and bisect each other.

How to Calculate Number of Rectangles in Grid?

Number of Rectangles in Grid calculator uses Number of Rectangles = C(Number of Horizontal Lines+1,2)*C(Number of Vertical Lines+1,2) to calculate the Number of Rectangles, Number of Rectangles in Grid formula is defined as the total count of rectangles that can be formed inside a grid created using a given set of horizontal and vertical lines from a plane. Number of Rectangles is denoted by N_Rectangles symbol.

How to calculate Number of Rectangles in Grid using this online calculator? To use this online calculator for Number of Rectangles in Grid, enter Number of Horizontal Lines (N_{Horizontal Lines}) & Number of Vertical Lines (N_{Vertical Lines}) and hit the calculate button. Here is how the Number of Rectangles in Grid calculation can be explained with given input values -> 1980 = C(10+1,2)*C(9+1,2).

FAQ

What is Number of Rectangles in Grid?

Number of Rectangles in Grid formula is defined as the total count of rectangles that can be formed inside a grid created using a given set of horizontal and vertical lines from a plane and is represented as N_Rectangles = C(N_{Horizontal Lines}+1,2)*C(N_{Vertical Lines}+1,2) or Number of Rectangles = C(Number of Horizontal Lines+1,2)*C(Number of Vertical Lines+1,2). Number of Horizontal Lines is the total count of given straight lines which are horizontally oriented on a plane & Number of Vertical Lines is the total count of given straight lines which are vertically oriented on a plane.

How to calculate Number of Rectangles in Grid?

Number of Rectangles in Grid formula is defined as the total count of rectangles that can be formed inside a grid created using a given set of horizontal and vertical lines from a plane is calculated using Number of Rectangles = C(Number of Horizontal Lines+1,2)*C(Number of Vertical Lines+1,2). To calculate Number of Rectangles in Grid, you need Number of Horizontal Lines (N_{Horizontal Lines}) & Number of Vertical Lines (N_{Vertical Lines}). With our tool, you need to enter the respective value for Number of Horizontal Lines & Number of Vertical Lines and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Number of Rectangles?

In this formula, Number of Rectangles uses Number of Horizontal Lines & Number of Vertical Lines. We can use 1 other way(s) to calculate the same, which is/are as follows -

Number of Rectangles = C(Number of Horizontal Lines,2)*C(Number of Vertical Lines,2)

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