Questions about rectangles and its properties.

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How to find one side of a rectangle, if I have other side and slope

So suppose I have the width of a rectangle that is 1000 cms and its slope that is at 20 degrees. How can I calculate the other length required for the height of this rectangle....
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2answers
17 views

Finding the greatest possible dimension of a rectangle

Here's the question: If the greatest possible distance between two points within a certain rectangular solid is 12, then which of the following could be the dimension of the solid? A) 3x3x9 B) 3x6x7 ...
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trigonometry - find coordinates of inner triangle after rotation

here is my situation: I have a rectangle I'm rotating 30 degrees counterclockwise, how could I use trig to get the 3 vertices (corners) and lengths of the purple triangle sides and hypotenuse ...
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3answers
209 views

Finding the area of the 4th triangle, given the areas of the other 3, and all the 4 form a rectangle

In one of my tutorial classes, when I was studdying in 9th class (I am in 10th now), our tutor gave us a problem saying it’s a difficult one, and to him, it was incomplete. This is that problem: ...
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1answer
17 views

find the distance of a point from the sides of a rectangle

I would like to find the distance of a point from the sides of a rectangle. here is various examples: t(x,y) is a point within the rectangle (WxH). We have two angles (1-3 angle is 90 and for Fig ...
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2answers
67 views

Maximum area of a rectangle

Two concentric circles have radii 13 and 15. Let ABCD be a rectangle, so that A and B lie on the larger circle, and C and D lie on the smaller circle. Find the maximum area of rectangle ABCD. I tried ...
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1answer
10 views

Work Out Height Based on Width and Ratio

I'm trying to work out the height of an image. I have this data available to me: width: 320 ratio: 0.66 Is it possible to work out the height based off the data ...
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1answer
48 views

Find the area of the shaded region

This is the Figure, $ABCD$ is a square , $AB = BC = CD = DE = 21cm$. $AC$ and $BD$ are the diagonals of the square. The two semi circles are drawn with $AD$ and $BC$ as diameter. Find total are of ...
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22 views

Find longer side of a rectangle with respect to another rectangle

So I have two rectangles: Rectangle R1 with width r1w and height r1h Rectangle R2 with width r2w and height r2h I can find the slope/aspect ratio of the two ...
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1answer
32 views

How to find the side for the biggest area?

Let $x$ be one side of a rectangle and $a$ its perimeter. We know that it's area is given by: $$ S = x\cdot\left(\frac{a}{2}-x\right). $$ $$ S=-x^2+ax/2$$ where a=-1, b= a/2 and c= 0 $$D=a^2/4$$ ...
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3answers
89 views

Squaring of the circle

From curiosity I read about enhancements of the squaring of the circle. Right now I do not see what is wrong with the following approach: Archimedes devised that the surface of a circle equals the ...
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1answer
78 views

Geometry: Construct a rectangle with area equal to a given triangle and with one side equal to a given segment.

So we have triangle, ABC, and line segment DE. We don't know anything about them other than ABC is a triangle of some sort and DE is a line segment. We're tasked with constructing a rectangle such ...
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39 views

Dividing rotated rectangle into equal area grid

I have a rotated rectangle that is represented by the coordinates of its 4 vertices (Actually represented by 4 lat-lon). I want to divide the rectangle into equal area grids. I need this to find the ...
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0answers
79 views

Geometry question: translating a rectangle according to a specific rule

Please take a look at the figure below. I have two line segments: a, which goes from point A to point B, and b, which goes from point B to point C. Each line defines a rectangle, which has width d and ...
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Largest rectangle bounded under a function

Let $f$ be a positive monotonically increasing real function in $[0,1]$. Let $F$ be the area under the curve of $f$ ($F=\int_0^1{f(x)dx}$) For every $x\in[0,1]$, let $G(x)=f(x)*(1-x)$ = the area of a ...
16
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1answer
221 views

Under what conditions will the rectangle of the Japanese theorem be a square?

In geometry, the Japanese theorem for cyclic quadrilaterals states that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle. Question. Under ...
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1answer
102 views

Geometrical calculation to determine size difference between two rectangles when rotating one

I've asked a programming question on StackOverflow here which should give you a good understanding why I'm trying to do this. I'm asking it here because it's now down entirely to the mathematics of ...
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1answer
164 views

Find other coordinates on a rectangle given 1 side length and 2 opposite points

I have two problems I'm hoping to solve with one equation for a game. This game uses a square for its key (rotates) but I'd prefer to treat it as a rectangle instead. I want to find the coordinates so ...
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1answer
24 views

Point in a rectangle

$ABCD$ is a rectangle and $P$ is a point in the same plane. If the perpendicular through $C$ to $AP$ and the perpendicular through $B$ to $DP$ intersect at $Q$, prove that $PQ \parallel AD$. ...
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1answer
36 views

Find length of side

I tried to solve this problem ... but i can't find answer. Anyone can help me? EBC=90 & DCB=90 & AHC=AHB=90
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1answer
33 views

Calculating rectangle having 2 coordinates and 1 length

How could I calculate the other 2 points if I have a rectangle with 2 points and 1 length given? ...
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1answer
70 views

How to evenly space a number of points in a rectangle?

Say I have a rectangle, with variable width and height, for example lets use: width = 20 height = 30 I would like to put n ...
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2answers
82 views

Finding the length of the side of the equilateral triangle

Here, ABCD is a rectangle, and BC = 3 cm. An Equilateral triangle XYZ is inscribed inside the rectangle as shown in the figure where YE = 2 cm. YE is perpendicular to DC. Calculate the length of the ...
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1answer
43 views

Deskew a rectangle

I'm having a "trigonometric" issue. I have as input an image that contains a skewed rectangle. The image is like a bounding box of the rectangle. like this: ...
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1answer
24 views

Geometry - Cyclic Quadrilaterals

Three points A,B,C lie on the circumference of the circle, with center as O. If angle(ACB) = 115 deg. Need to find angle (BOC)? Please post your approach?
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Collision Detection in Finite but Limitless Space

Doing collision detection on two arbitrary rectangles is easy, given their coordinates and dimensions. In regular 2d-space, that is. But what about "finite but limitless" space, say a screen area ...
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2answers
106 views

What is the correct definition of Area?

How is the area of a rectangle: length $\times$ breadth? We know that other areas can be derived from it. Also, the area under curves uses the area of rectangles as a basis.
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Two questions about triangle that blocked at rectangle…

The area of the triangle is equal to the half area of the rectangle? The center point of the triangle is same as the center point of the rectangle? About 2 - if not, how do I calculate the center? ...
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155 views

How would I calculate the area of a rectangle on a sphere using vertical and horizontal angles?

Imagine a sphere being one's eyeball and the rectangular area being the picture of one's view. Like putting a name tag sticker on a balloon. How can I find the area of the rectangle on the sphere?
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1answer
16 views

Determining the distance across a rectangle for an arbitrary angle

I'm trying to determine the 'diameter' or distance across a given rectangle for a given angle. Ideally there should be a function f(theta) that takes a polar angle and determines the distance across ...
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1answer
124 views

How to find height, width, length of rectangular prism given SA and longest diagonal?

I've started seeing this type of question an awful lot. I made two equations (w is width, l is length and h is height) √w^2+l^2 + h^2= 64 2wl + 2lh + 2wh = 14 However, I'm not sure where to go from ...
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1answer
30 views

Rectangle division into shapes and connecting adjacent shapes with non-intersecting lines

Rectangle is divided into several non-convex shapes. Adjacent shape's centroids are connected with straight lines. For example (here centroids are approximate): Could it be that some of those line ...
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1answer
27 views

How can I do complex table size calculations?

For instance, I want to know: What is the most efficient way to present 256 cells in a 16:9 table, giving each cell maximum readability? In the above scenario, each cell must be sized ...
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2answers
104 views

Area of one of four regions within a rectangle

There is a figure below (a rectangle). You can see different colors depicting different regions of the figure. The labels on the top of a region defines the area of that region. Can you find the ...
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1answer
15 views

Want to make a rotating background, find the minimum size in relation to the screen.

I am making a game, and want to make a rotating background. I want to find the minimum size the background needs to be in order to not get cut off in the middle of the rotation, so I went for a 45deg ...
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1answer
26 views

Find the size of squares cut from a box.?

This has been taking me days to do and I really want to do it for test practice. I actually have absolutely no idea how to even start this, so if I can get a hint, advice, or something to start me ...
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1answer
63 views

Disprove the possibility of such a triangle.

The image is not that good, but, consider the following figure to be true without actually constructing it,how can one person find a $fault$ in it. The blue colour represents perpendicular, The ...
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0answers
40 views

Compressing an image by merging pixels [duplicate]

Let's say you have an image with dimensions (height, width) $h,w$ pixels. It is stored in a table $T[y][x]$ Unfortunately, the software you are using to generate this image can only use rectangles. ...
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1answer
46 views

Area of rectangle from area of square?

The definition of area usually include the area of a rectangle definition. Can one replace it with "the area of a square of side $a$ is $a^2$"? That is can one find the area of a rectangle in this ...
2
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1answer
50 views

Is there an equation to find the angle of the diagonal in a rectangle?

If we have a rectangle of length 5 and height 5 the angle of the diagonal would be 45°. We know this is true but how can we arrive at this conclusion mathematically?
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Find if the given size of the rectangle fits on the rectangle

Given a rectangle of size row = 3 and col = 2 which are occupied by other rectangles as in figure. The shaded region in green are occupied. Now what I want to find is, if a rectangle of size (p = 2 ...
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1answer
47 views

Calculate the width and height of a rectangle, given its diagonal and area

Here's my problem: "In a rectangle, the diagonal is 6 and area 14. The perimeter is: a) 10 b) 14 c) 16 d) 18 e) 20. So I know that $x^2 + y^2 = 36$, and that $xy = 14$, but I'm having problems ...
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1answer
36 views

Size of minimal covering, overlapping and disjoint

There are two ways to cover a geometric shape with primitive units: you can allow the units to overlap, or require that they be disjoint. Of course the number of units in the case of disjoint covering ...
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Find bounding box dimensions around rotated object

Consider the following rectangle with dimensions 320 by 130. After rotating the rectangle 10 degrees clockwise from the center (x: 160, y: 65), it looks like this. My question is: How do ...
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3answers
85 views

Inscribe a rectangle inside an ellipse

A rectangle is to be inscribed inside a horizontal ellipse (whose major or minor axis is parallel to x axis). Is the horizontal orientation of the rectangle (two sides parallel to x axis) the only ...
2
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2answers
102 views

Finding a 3rd coordinate of the rectangle points in 3d

I have a 4 3-D-points, each of them has only 2 of 3 known coordinates, as follow (? is unknown here): P5 (P5x, P5y?, P5z) P6 (P6x, P6y?, P6z) P3 (P3x, P3y, P3z?) P4 (P4x, P4y, P4z?) They build ...
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69 views

internal rectangle area intersected by a circle

I need to compute the internal rectangle area intersected by a circle like (the blue area) on these 3 examples: I know every vertex (x,y) coordinate and then their distance from circle center but ...
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1answer
33 views

Divide-and-conquer on a rectilinear polygon

A rectilinear polygon can be characterized by its cover number - the smallest number $k$ such that the polygon can be covered by $k$ possibly overlapping squares. For example: For a square, $k=1$. ...
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3answers
105 views

Volume of a rectangular prism's walls

Sorry if this is an obvious question... I have been trying to figure this out for a little while and come up with nothing... If I have a rectangular prism, say $5\times10\times12$ meters, it has a ...
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10answers
13k views

Why is a rectangle a parallelogram, but a parallelogram is not a rectangle?

It confused me that a parallelogram is never considered a rectangle, yet a rectangle is considered a special case of a parallelogram. How is this possible?