# Questions tagged [rectangles]

Questions about rectangles and their properties.

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### How do you prove that a specific shape in a regular octagon is a rectangle? [closed]

In regular octagon ABCDEFGH, how do you prove that ADEH is a rectangle? This is assumed in many problems that find the area of an octagon. Since AD and EH are symmetrical diagonals, they are equal, ...
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### How to determine the elevation at the edges of a tilted rectangle?

The rectangle is slanted in direction B to C and the elevation at point B (between the edge and the floor) is 1.2 cm. C is the only edge that touches the floor. How to determine the elevation at ...
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### Elliptical Grid Mapping in Shader

I wanted to make a Elliptical Grid Mapping Shader, but it is not a perfect square and it is rotated. If i multiply the coords by sqrt(2.) and divides them after again, it is an square, but still ...
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### A square divided into congruent rectangles

Can a 1*1 unit square divided into congruent rectangles with irrational side lengths? The answer might seem trivial, but there are two irrational numbers in which both their sum multiple is rational; ...
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### Square with irrational side partitioned into rectangles

Given a square with sidelenght $\sqrt{2019}$ partitioned into finite number of rectangles one needs to show that at least one of them must have both sides irrational. It's obviously one of them must ...
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### Calculating the corners of a rotated outer rectangle that encapsulates minimally an inner rectangle.

I have two rectangles that start as the same size. When I rotate one of these rectangles I want it to encapsulate the other rectangle taking up the minimum possible area. The coordinates of the ...
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### Cutting Up a Rectangle and Piecing Together a Square of the Same Area

Original Question Given a rectangle $ABCD$ where $AD=a$ and $AB=b$, cut up the rectangle into some pieces such that piecing the pieces back together will form a square with the same area as the ...
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### Center position of an orthogonal rectangle that has a side or corner touching a circumference

I need to find how distant the center of an orthogonal rectangle is from the center of a circle, given a specific angle. The dimensions of the rectangle are proportional to the circle radius, so they ...
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### Find the number of rectangles not containing the shaded square [closed]

I wish to find the number of rectangles that don't contain the shaded square: Image of the grid: I used the way of finding the total number of rectangles and subtracting the rectangles containing the ...
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### Prove that triangles $VAC$ and $VBD$ have equal areas and equal perimeters....

The question Let $VABCD$ be a quadrilateral pyramid with a rectangular base. $\angle AVC =\angle BVD$ prove that triangles $VAC$ and $VBD$ have equal areas and equal perimeters. The idea Because the ...
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### Covering a circle using rectangles

What is the maximum area that can be covered with $3$ rectangles inside a radius $1$ circle?(i.e. maximum area $=\pi$) The rectangles can be any length and height you want, and can rotate and reflect. ...
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1 vote
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### Hyperplane Separation Theorem for non-axis aligned rectangles?

I'm trying to understand how the Hyperplane Separation Theorem works. I found a function on MATLAB that implements it, accepting the parameters rect1 = [0 0; -1 3; 6 4; 7 1]; rect2 = [12 0; 14 1; 13 ...
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### A function to transform a rectangle into a triangle and vice versa.

I have two input variables, let's call them x and y, which are the inputs to a function. There is a condition for these two inputs: x+y must be equal to or less than 1. So, my input space would look ...
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### Is the converse of Vertically opposite angles true?

When two straight lines intersect the vertically opposite angles are equal. But, can we say that, if the vertically opposite angles of two lines are equal then the lines are straight? The angles ...
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### how many rectangles in a circle with defined measurements

example of rectangles in circle i have various size plates as follows 12m 10m 8m 6m 4m i need to be able to calculate how many rectangles i need in a quardrant(can be mirrored for other quadrants) the ...
Can anyone help me find an approach to deriving the equation $$\left\lvert \frac{x}{p}+\frac{y}{q} \right\rvert + \left\lvert \frac{x}{p}-\frac{y}{q} \right\rvert = c$$ for a rectangle in the ...