Questions about rectangles and its properties.

learn more… | top users | synonyms

0
votes
2answers
36 views

Why can't I know if the figure is a rectangle, if angles c+d=180 and c=d?

I have a four sided figure, abcd (see the image, and ignore the EF part), where I know that angles c+d=180 and c=d. However, this isn't enough information to decide if this is a rectangle - why is ...
0
votes
2answers
34 views

What would be the area of this Red Marked points? And how to calculate this?

I have been given the length $L$ and the width $W$ of a rectangle and the radius $R$ of circle which is situated in the center of the rectangle . I need to find the area of the red marked portion. ...
2
votes
0answers
29 views

Fitting Rectangles

I have a quantity of small rectangles I need to fit in a larger rectangle frame. I need an equation to figure out what is the maximum size I can make the small rectangles before they are all too big ...
2
votes
1answer
36 views

An interesting geometry problem with midpoints and perpendicular lines in a rectangle

I saw this question from a student's geometry homework. And I was thinking whether there was an efficient method to solve the question. We are supposed to prove $DM \perp MN$. My thinking is to ...
-1
votes
1answer
29 views

Can I find out the angles of a rectangle given the sidelengths and that 2 of the sides are parallel?

Not really a big brain when it comes to math. First question here... hope it meets the standards. Let's say I've got a quadrilateral, I know the side lengths, and I know two of the sides are ...
0
votes
0answers
12 views

Optimized placing of same-size squares into rectangles

Suppose that we have several squares of the same size. We want to draw n rectangles (red and yellow rectangles here) to contain these squares. The goal is to have ...
0
votes
1answer
30 views

Calculating relative position of points when zoomed in and enlarged by a rectangle

There is a rectangle, defined by the top left point $R1(0, 0)$ and the bottom right point $R2(200, 200)$ (the $y$ $axis$ is inverted). In that rectangle, there are some points $P1(100, 100)$, $P2(50, ...
1
vote
1answer
47 views

Weyl's asymptotic law for eigenvalue on the rectangle $D = \{0 < x < a, 0 < y < b \}$ - $N(\lambda) \geq \frac{\lambda ab}{4 \pi} - C \sqrt{\lambda}$

I have a few difficulties understanding the example on the rectangle in the book Strauss W.A. Partial differential equations - an introduction (Wiley, $2008$, $2$nd Ed.) page $326$. I've managed to ...
0
votes
0answers
13 views

A tesselation where four parallel rectangles meet at each vertex

If we tile the plane with parallel rectangles that are translated copy of the same rectangle, then each point is either inside a tile, or on a segment common to two adjacent tiles, or a corner common ...
-1
votes
0answers
30 views

How to fit small squares in the big one? [closed]

Suppose, I have a square S with height H and width W. Also I have another square ...
0
votes
1answer
18 views

Get the width and height of the inner well aligned rectangle after rotation

I'd like to get the width and height of the red rectangle with this constraints: Maximize the area of the red rectangle The center of the rotation is the center of the original (dotted) rectangle. ...
3
votes
3answers
81 views

How to show that any rectangle in ellipse must be oriented parallel to axes?

A problem which is often given as an exercise for students learning about calculus and finding extrema, is to find maximal possible area of a rectangle inside an ellipse. Such question was asked, for ...
0
votes
0answers
47 views

Approximate area of overlap of two rotated rectangles

I need to estimate the overlap ratio of two rectangles, each one with arbitrary size and orientation. I know how to perform the exact computation, using the Sutherland-Hodgman algorithm, which can be ...
0
votes
1answer
27 views

How big do squares need to be to fit a box, tesselating, with minimal remainder?

A geometry question that I feel utterly defeated by. I'm trying to design a responsive user interface that efficiently fits a variable number of square elements on a screen, by adjusting the size of ...
1
vote
1answer
25 views

Cut corners from rectangle to get box with max volume

I've got a rectangle (no informations about the box, volume box etc.). I need to find how much should I cut from the rectangle to get a box with maximum volume, so I need to find $x = ?$ At the ...
1
vote
1answer
24 views

Consider a rectangle with vertices at E,F,G and H.

Consider a rectangle with vertices at E, F, G and H. Suppose $\overrightarrow{EF}$ = p and $\overrightarrow{FG}$ = q. Express each of the vectors EH, GH, FH and GE in terms of p and q. Hi everybody. ...
2
votes
1answer
28 views

What is the minimum radius $r$ of two intersecting circles that are spaced $x$ apart that completely enclose a square of length $w$?

Let's say we have two circles whose centers are spaced a fixed $x$ units apart from one another. Both circles have a radius $r$. Our goal is to identify the minimum value of $r$ so that the ...
2
votes
2answers
80 views

How do you calculate the area of the intersection between a rectangle and a doughnut?

I'm dealing with an engineering problem, involving concentric pipes, with air flowing through the outer pipe (doughnut). I need a cross-beam to support the inner pipe, so I need to calculate how much ...
0
votes
0answers
18 views

Scale a rectangle about a point considering reflection

Given a rectangle of width $(w_0)$, height $(h_0)$, left $(x_0)$, top $(y_0)$. How do I scale it from an origin $(x_1,y_1)$ with a scale factor of $(w_1, h_1)$ taking into account reflection? This ...
0
votes
1answer
108 views

How can you find the distance between the center and edges of a rectangle - a line from centre to a edge at an angle $\theta$?

I have a case where I know the coordinates $(x,y)$ of the center of the rectangle and its edges where the line is dropped anywhere on the edges $a(x_1,y_1),b(x_2,y_1),c(x_1,y_2),d(x_2,y_2)$. Say I ...
0
votes
1answer
24 views

Area formulae of various shapes

In the definition of perimeter of a shape, we have a very clear view. Perimeter is nothing but the total length of the boundary of a given shape. So formulae for various shapes are also very clear. ...
1
vote
1answer
56 views

Filling a rectangle with 0/1 (constraints on columns/lines sums)

Let's consider a $n \times m$ rectangle wich has to be filled in by $0$s and $1$s. The sum of the values contained in each colum/line is known. Here is an example: This is a solution: Does ...
1
vote
0answers
63 views

Length and width of shadow of rectangular plane

A book that I've read shows how to find the area of the shadow cast by a sphere and ellipsoid. The spherical shadow makes sense; its simply the area of a circle (which would be the sphere's shadow) ...
0
votes
1answer
20 views

The rectangle-partition number and the number of horizontral edges

The rectangle-partition-number of a rectilinear polygon $P$ is the smallest number of pairwise-disjoint axis-parallel rectangles required to cover $P$. Some examples: (in the last example, $P$ is ...
1
vote
3answers
34 views

solving rectangle

Diagonal of a rectangle is $13$ cm. If we extend the length of the rectangle for $4$ cm and width for $7$ cm, then diagonal will be longer for $7$ cm as well. Find sides (length and width) of the ...
0
votes
1answer
132 views

How to divide a large rectangle into N smaller rectangles

I would like to divide a NxMpx rectangle(matrix) into X piece different size smaller rectangles. X is a variable so it dosn't have a fix value.The smaller rectangles must fill the 80-90% area of ...
0
votes
2answers
64 views

Find the sum of the areas of all rectangles whose area is tripled when three units are added to the height and two units are added to the length

A rectangle has all sides of integer length. When three units are added to the height and two units to the length, the area of the rectangle is tripled. What is the sum of all the original areas of ...
1
vote
1answer
78 views

Dimensions of a rectangle containing a rotated rectangle

Given sides a, b, and an arbitrary rotation Θ (0 - 360 degrees) around the centerpoint of the rectangle, how would I calculate sides A and B of a containing rectangle?
0
votes
2answers
68 views

How to keep aspect ratio and position of rectangle inside another rectangle?

This problem has plagued me for many years. Given two rectangles how do I resize the first to fit into the second while preserving the aspect ratio? The second rectangle could be bigger or smaller ...
0
votes
2answers
35 views

Find point on line between two rectangle centers where line hits edge

I have two rectangles as in the picture below which can be located anywhere relative to each other. I have the coordinates of the rectangle centers (c1 and c2) and the lenght/height of both rectangles....
1
vote
2answers
138 views

Can you construct a rectangle with a given side, equal to a square?

In Euclid's Elements, Book 2, Proposition 14, We are shown how to construct a square from a given rectilinear figure. This allows us to square a rectangle. Is it possible to do the inverse, creating ...
0
votes
1answer
50 views

How to find the value of x given the following rectangular that has been divided into 4 parts?

A rectangle is divided into sections with the area shown. What is the value of X? At first I didn't know what i would do than i noticed that X is 1/4th of the rectangular . But I don't know what to ...
0
votes
2answers
85 views

What is the number of tiles needed to cover a rectangular floor given diagram?

A square tile measures 6 inches by 6 inches. What is the least number of tiles needed to cover a rectangular floor area of 9 feet by 12 feet? So the first thing i tried to do was divide 9 by 6 and ...
1
vote
2answers
59 views

If I have a vector inside a rectangle, how do I tell which side of the rectangle the vector will hit?

I'm trying to solve an issue where I basically have a vector inside of a rectangle. I want to figure out if the vector continues its trajectory, what side will it strike? The vector is given as an (x, ...
0
votes
1answer
52 views

Finding suqares in the rectangle $(0,0,1,1)$ which are “divided with” $\frac{\pi}{4}$ by the unit circle.

I want to write an algorithm which calculates the following: Find all suqares $(x_0,y_0,x_1,y_1)$ which are "in" the suqare $(0,0,1,1)$ and are divided by the unit circle so that their inner area ...
0
votes
1answer
41 views

How to find the angle of a rectangle vertex

before I go further I want you to know that I'm developing a collision detection system in a programming language (Javascript). I'm not used to math terms (it was like 10 years ago when I was in ...
1
vote
2answers
56 views

Question on circles inscribed in a rectangle

In rectangle $ABCD$, $AB = 8$ and $BC = 20$. Let $P$ be a point on $AD$ such that angle $\measuredangle BPC = 90^\circ$. If $r_1, r_2, r_3$ are the radii of the incircles of triangles $APB, BPC$ and $...
1
vote
1answer
26 views

Finding which diagonal area of a rectangle you are in

I am trying to calculate which diagonal half a user has clicked within a box using x and y co-ordinates. I have found out how to do this in one diagonal direction, but can't figure out how to change ...
7
votes
2answers
172 views

Partition of a rectangle into smaller rectangles, with their diagonals forming a loop

The Big and the Small Kingdom are both rectangular islands and divided into rectangular landscape. In each province there is a road that runs along one of the diagonals. On each island exist roads ...
0
votes
1answer
180 views

Find points of Rectangle given two diagonal points and a normal in 3D

I'm developing a geometry framework in a program I'm working on that contains all the good stuff like vectors, points, lines, planes, polygons, etc. I was attempting to create a rectangle object, but ...
0
votes
0answers
8 views

Moving overlapping rectangle by a vector portion

I have rectangles: $S$, $T$, and $R$, described by their top left and bottom right corners, such as $S = ([S_{x1},S_{y1}], [S_{x2},S_{y2}]$), etc. The rectangles $S$ and $T$ are connected by a line ...
1
vote
1answer
10 views

Prove that a polyrectangle in an open set has a superset polyrectangle.

Theorem: Let $S \subseteq \mathbb{R}^n$ be an open set. Let $P \subset S$ be a polyrectangle. Then there exists another polyrectangle $P'$ such that $P \subset P' \subset S$. A polyrectangle ...
3
votes
4answers
817 views

How do I find the maximum perimeter of a rectangle inscribed in an ellipse?

The problem I've been stuck on is this: A rectangle is inscribed in the ellipse $$\frac{x^2}{20} + \frac{y^2}{12} = 1$$ What is the maximum perimeter of the rectangle? I don't even know if I'm ...
-1
votes
2answers
104 views

Scale a rectangle from a point other than its center [closed]

How do I scale a rectangle from a point other than the centre of the rectangle? Specifically, I am trying to determine the new X and Y position of a rectangle after having rescaled it, taking into ...
1
vote
0answers
52 views

Filling a rectangle with congruent squares in two columns

I have a rectangle. This rectangle is divided into two columns; the widths of these columns are not necessarily equal, and are not known. I want to fill the rectangle with squares. The number of ...
18
votes
2answers
251 views

Largest rectangle not touching any rock in a square field

You want to build a rectangular house with a maximal area. You are offered a square field of area 1, on which you plan to build the house. The problem is, there are $n$ rocks scattered in unknown ...
0
votes
0answers
73 views

Determine what is length and what is width of a rectangle

I have an algorithm to write for an app. So I am given a reference rectangle with known width and length and I have bigger rectangle which sides I have to determine, where one side is known. I realize ...
2
votes
1answer
39 views

Covering a rectangle with circles

jgkjgbjb efewfesf fsefesfwsf sf swfsfsfsref sfsfsfsf
-5
votes
1answer
42 views

How to find whether a rectangular keyboard can fit into a square bag? [closed]

Will a 18.6'' x 1.3'' x 6.8'' keyboard fit into a 15''x15'' bag? If yes, how will it have to be oriented? If no, what size bag would I need for the keyboard to fit? What I have figured already is ...
0
votes
1answer
27 views

Is this Quadrilateral possible?

Is this figure possible to achieve? $AD > BC$; $\angle BCD$ = $\angle BAD$ = $90^{\circ}$ . And this is supposed to be a closed quadrilateral. I'm confused as to whether this is viable - since $...