Questions tagged [quadrilateral]
For questions about general quadrilaterals (including parallelograms, trapezoids, rhombi) and their properties.
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Quadrilateral Interpolation
The simplest finite element shape in two dimensions is a triangle.
In a finite element context, any geometrical shape is endowed with an interpolation,
which is linear for triangles (most of the time),...
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Any employment for the Varignon parallelogram?
The midpoints of the sides of an arbitrary quadrilateral form a parallelogram, which is called the
Varignon parallelogram of the quad.
While answering a question about
Quadrilateral Interpolation it ...
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Does the square or the circle have the greater perimeter? A surprisingly hard problem for high schoolers
An exam for high school students had the following problem:
Let the point $E$ be the midpoint of the line segment $AD$ on the square $ABCD$. Then let a circle be determined by the points $E$, $B$ and ...
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Area of a square inside a square created by connecting point-opposite midpoint
Square $ABCD$ has area $1cm^2$ and sides of $1cm$ each.
$H, F, E, G$ are the midpoints of sides $AD, DC, CB, BA$ respectively.
What will the area of the square formed in the middle be?
I know that ...
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Collinearity problem (Newton-Gauss line)
I had some troubles with this problem :
Let $ABCD$ be a convex quadrilateral. $M$ and $N$ are the midpoints of
the diagonals $AC$ and $BD$. The sides $AB$ and $CD$ are extended
until they ...
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Maximum area of a square in a triangle
I want to calculate the area of the largest square which can be inscribed in a triangle of sides $a, b, c$ . The "square" which I will refer to, from now on, has all its four vertices on the sides of ...
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Is there a formula to calculate the area of a trapezoid knowing the length of all its sides?
If all sides: $a, b, c, d$ are known, is there a formula that can calculate the area of a trapezoid?
I know this formula for calculating the area of a trapezoid from its two bases and its height:
$$S=...
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Trisect a quadrilateral into a $9$-grid; the middle has $1/9$ the area
Trisect sides of a quadrilateral and connect the points to have nine quadrilaterals, as can be seen in the figure. Prove that the middle quadrilateral area is one ninth of the whole area.
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If a quadrilateral has a pair of equal opposite sides, and a pair of equal opposite angles, then is it necessarily a parallelogram?
I’m sorry I couldn’t upload a photo, so I’ll try to explain it as best as I can.
The quadrilateral has a pair of opposite and equal sides, and has a pair of opposite equal angles (85 degrees in the ...
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What is the maximum area of a square inscribed in an equilateral triangle?
What is the maximum area of a square inscribed in an equilateral triangle?
Please post the approach to solve the above question.
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The concave quadrilateral and the slopes of its sides
Suppose a plane quadrilateral ABCD without sides parallel to y-axis, and let $m_1, m_2, m_3, m_4$ be the slopes of the equations of sides AB, BC, CD, DA (the cartesian axes being orthogonal or ...
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Relationship of aspect ratio to the homography matrices between a rectangle and an arbitrary quadrilateral
I've been reading everything I can on the perspective mapping between a 2D rectangle and the projection onto the plane in 3D space of a rectangle.
I've learned that any such quadrilateral resulting ...
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Area of parallelogram = Area of square. Shear transform
Below the parallelogram is obtained from square by stretching the top side while fixing the bottom.
Since area of parallelogram is base times height, both square and parallelogram have the same area.
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A conjecture involving prime numbers and parallelograms
As already introduced in this post, given the series of prime numbers greater than $9$, let organize them in four rows, according to their last digit ($1,3,7$ or $9$). The column in which they are ...
user559615
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Why study quadrilaterals?
My niece is in the 10th grade, and they have to do lot of theorems related to quadrilaterals. And, I was surprised to know that they have to learn by rote some theorems. This has made her feel that ...
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