Vertices: E (-2, -1); F (-4, 3); G (1, 5); and H (3, 1).
Plot these points in a coordinate system and connect them. The quadrilateral EFGH is formed.
The slope of the line where the side EF lies is -2.
[(3 - -1)/(-4 - -2)] = 4/-2 = -2
The slope of the line where the side HG lies is -2.
[(5 - 1)/(1 - 3)] = 4/-2 = -2
Thus the opposite sides EF and HG of the quadrilateral EFGH are parallel.
The slope of the line where the side EH lies is 2/5.
[(1 - -1)/(3 - -2)] = 2/5
The slope of the line where the side FG lies is 2/5.
[(5 - 3)/(1 - -4)] = 2/5
Thus the opposite sides EH and FG of the quadrilateral EFGH are parallel.
Since any of the slopes is not a negative reciprocal of the others, then the two adjacent sides are not perpendicular. And if we look at the diagram, we clearly see that this quadrilateral can be a parallelogram.
The length of the side EF is square root of 20.
Square root of [(5 - 1)^2 + (1 - 3)^2] = Square root of [4^2 + (-2)^2] = Square root of 20.
The length of the side HG is square root of 20.
Square root of [(3 - -1)^2 + (-4 - -2)^2] = Square root of [4^2 + (-2)^2] = Square root of 20.
Thus, the opposite sides EF and HG of the quadrilateral EFGH are congruent.
Two other parallel sides, EH and FG, must be congruent also, since they intersect two other parallel lines (their length is equal to square root of 29).
So we verified that the quadrilateral EFGH is a parallelogram.
It depends on the shape of the area. Four sides of a quadrilateral - if that is what the given measurements are - do not determine a unique shape.
With four sides given a quadrilateral is not clear defined. Infinite are possible. You need the length of one diagonal in addition to figure out the area.
4 times 4
Pick a vertex of the original shape.Draw a perpendicular to the given line.Double the length of this perpendicular. The end point is the image of the original vertex.Repeat for all other vertices of the original shape.Join the vertices of the image.
If all the vertices and edges of a graph A are in graph B then graph A is a sub graph of B.
Suppose a quadrilateral is given using its vertex coordinates. It will be a triangle if three vertices are collinear, that is are on the same line.
A square would fit the given description
The answer depends on the shape of the quadrilateral and the form in which that information is given: for example, lengths of sides and angles, coordinates of vertices.
12 vectors, unless it is a parallelogram (13 if you include the null vector). If the quadrilateral is a parallelogram there will be two fewer.
The code given on army based equipment to determine its classification
A square-based pyramid would fit the given description. (A triangular prism would have 9 edges and 6 vertices)
It is not possible to determine the area of a quadrilateral given only the length of its four sides.
In geometry, a cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. The vertices are said to be concyclic. In a cyclic quadrilateral, opposite angles are supplementary (their sum is π radians or 180°). Equivalently, each exterior angle is equal to the opposite interior angle. The area of a cyclic quadrilateral is given by Brahmagupta's formula as long as the sides are given. This area is maximal among all quadrilaterals having the same side lengths. Ptolemy's theorem expresses the product of the lengths of the two diagonals of a cyclic quadrilateral as equal to the sum of the products of opposite sides. In any convex quadrilateral, the two diagonals together partition the quadrilateral into four triangles; in a cyclic quadrilateral, opposite pairs of these four triangles are similar to each other. Any square, rectangle, or isosceles trapezoid is cyclic. A kite is cyclic if and only if it has two right angles. ----Wikipedia
When the given vertices are plotted and joined together on the Cartesian plane they will form a 4 sided quadrilateral whose diagonals intercept each other at right angles and so multiplying the lengths of the diagonals divided by two will produce an area of 80 square units.
The given points when plotted on the coordinated grid is a rectangle
From the given coordinates it would form a line segment whose end points are (5, 2) and (0, 2) and so there is no 4 sided quadrilateral.
A quadrilateral is the name given to any 4 sided polygon.