Questions about rectangles and its properties.

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3
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1answer
58 views

Area of the shaded part in rectangle

The question asks you to determine the shaded part of the rectangle in terms of x. please will someone help with this problem, i have spent a while on it with not much progress.
1
vote
1answer
50 views

Area of overlapping squares

I'm working on a programming project and got to the point where I need to find how much is the blue square overlapping each of the other 9 squares. The squares' sides(including the blue one's) are ...
1
vote
1answer
27 views

Similar quadrilaterals in rectangle

While working on a problem on finding the shaded region in a rectangle, I realized that if a line cuts a rectangle into two quadrilaterals, then these two quadrilaterals are similar as the opposite ...
1
vote
1answer
43 views

Compute ratio of a rectangle seen from an unknown perspective

TL;DR: Given 4 points on a two dimentional plane, representing a reclangle seen from an unknown perspective, can we deduce the width / height ratio of the rectangle ? Details: From a picture, and ...
5
votes
2answers
105 views

How to solve this riddle?

How to solve this riddle? All rooms have the same shape and size. Every room has one entrance, and two exits: one on the left, and one on the right (on opposite directions). Both exits lead to a ...
1
vote
0answers
56 views

Calculating the Area of a Circle Occupied by a Rectangle

This is a question regarding how to calculate the area of a circle occupied by a rectangle when that rectangle is larger than the circle (see this link for a example image ...
0
votes
1answer
84 views

Area of Circle Overlapped by Rectangle

I'm trying to determine 'how much' (as a percentage) a 2D rectangle fills a 2D circle. Actual Application: I was comparing the accuracy of some computer game weapons by calculating the max possible ...
2
votes
5answers
576 views

Does rotation of a rectangle keep it rectangular?

If I rotate a rectangle by 45°, does it stay rectangular or become something else? I mean do 90° angles stay 90°? I am asking this question because I have some results where the rotated rectangle ...
2
votes
2answers
22 views

2D geometric relation in a rectangle

I'm trying to implement the Sakoe & Chiba's global constraint for the Dynamic Time Warping algorithm but I'm stuck with a geometrical problem : I'm trying to find the value of d given a, b and c. ...
9
votes
4answers
513 views

Check if a point is inside a rectangle (not knowing the coordinates, but knowing distances to vertices)

I have to solve the following problem: I have 4 points (A, B, C, D) which form a rectangle, but I do not know their coordinates. I have another point (X), I do not know its coordinates either, but I ...
3
votes
3answers
69 views

Prove this is a rectangle

Suppose we have quadrilateral $ABCD$ where $m\angle A = m\angle B = 90^\circ$ and $AB \cong CD$. Is this figure always a rectangle? If not, can someone give a counterexample? I tried drawing the ...
0
votes
0answers
21 views

Highest area rectangle in a rectangle trapezoid

There is a rectangle trapezoid with base sizes 8 and 24 and height of 12. Is there a way of finding highest area rectangle inside a trapezoid which 2 points would be in sides of a trapezoid? I ...
0
votes
1answer
28 views

Resizing Rectangular Boxes With Mouse

I'm creating a system that allows users to create objects on the screen (as rectangles) and move them around and resize them using the corners and the mouse. My only problem is, when one of the ...
1
vote
2answers
29 views

How to detect all points of rectangle by given one point A, height, width, and angle between AC and X axis? [closed]

How to detect points B, C, D of rectangle with given point A, height, width and angle L between AC and X axis.
0
votes
3answers
102 views

How to check if two rectangles intersect? Rectangles can be rotated

How to check if two rectangles intersect? Each rectangle is defined by three points in 2d space. The rectangles can be rotated around any point as on the image below.
1
vote
0answers
25 views

Finding optimal height for objects in 2D packing

I have a problem that I need to find the right algorithm for and I am not sure which avenues are going to be easiest. I have a 'row' of fixed height and we can assume infinite length. fig.1 ...
0
votes
1answer
60 views

In Neutral Geometry, prove that the opposite sides of a rectangle are congruent.

I'm having some trouble proving a theorem of Neutral Geometry. First, allow me to clearly state what we are allowed to assume in Neutral Geometry: Hilbert's incidence axioms Hilbert's order axioms ...
5
votes
0answers
29 views

Does a point quadrilateral form a rect in 3D space?

I have 4 points with x and y coordinate and would like to find out a way to check if given quadrilateral would be a rectangle in 3D space. I tried a bunch of conditions, but there was always and edge ...
0
votes
0answers
23 views

Maximize the intersection over union of oriented rectangles

I have an oriented rectangle in the form region=(x1,y1, ..., x4, y4) I want to know which is the axis-aligned rectangle with the same center that maximize the intersection over union of the areas of ...
1
vote
0answers
51 views

Find maximum width of a rectangle contained with another (diagonally)

It appears that the question of figuring out if a rectangle will fit inside of another, specifically at a diagonal, has been asked before. As such, utilizing the equation linked here, I was able to ...
0
votes
1answer
97 views

Dimensions of a paddock (3 sides of a rectangle) to enclose maximum possible area

I need help with Qs 4, 5 and 6!! Three sides of a rectangular paddock are to be fenced, the fourth side being an existing straight water drain. If 1000m of fencing is available, what dimensions ...
0
votes
1answer
42 views

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....
0
votes
2answers
40 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 ...
0
votes
0answers
10 views

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 ...
5
votes
3answers
274 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: ...
1
vote
1answer
23 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 ...
2
votes
2answers
75 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 ...
0
votes
1answer
20 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 ...
0
votes
1answer
129 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 ...
0
votes
1answer
27 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 ...
0
votes
1answer
35 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 $$D=a^2/4$$ ...
0
votes
3answers
100 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 ...
1
vote
1answer
147 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 ...
0
votes
0answers
47 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 ...
0
votes
0answers
103 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 ...
7
votes
0answers
72 views

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
votes
1answer
230 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 ...
2
votes
1answer
154 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 ...
0
votes
1answer
272 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 ...
2
votes
1answer
25 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 $PQ \parallel AD$. ...
0
votes
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
0
votes
1answer
45 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? ...
0
votes
1answer
114 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 ...
2
votes
2answers
100 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 ...
0
votes
1answer
59 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: ...
0
votes
1answer
25 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?
0
votes
1answer
47 views

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 ...
3
votes
2answers
117 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.
0
votes
0answers
30 views

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? ...
1
vote
2answers
225 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?