What Are 4 Sided Shapes Called – Polygons are among the first shapes we learn to draw as children, and they appear all around us. Polygons can be regular or irregular. It can be simple or complex, convex or concave. They can be regular shapes you see in geometry textbooks, or odd shapes like darts and bow ties.
The word “polygon” means “many-edged” from the Greek. To be a polygon, a flat, closed shape must consist only of line segments to form its sides. So a circle or any shape with a curve is not a polygon.
What Are 4 Sided Shapes Called
Regular polygons have congruent sides and interior angles. Each side is the same length as every other side, and each interior angle is equal to all other interior angles. The number of regular polygons is infinite.
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Irregular polygons do not have congruent sides and angles. The ground plane on a softball or baseball field is a regular pentagon because it has five sides and two 90° angles.
Convex polygon closes off the interior without appearing “dented”. None of the inside corners point inwards. In geometry, you can have a four-sided polygon pointing outwards in all directions, like a kite, or you can have four equal sides, so two sides point inward, forming an arrow. The kite is convex; The arrow is hollow.
Each interior angle of a convex polygon is less than 180°. A concave polygon has at least one angle greater than 180°. Imagine a simple hexagonal bow tie (6 sides). It will have two interior angles that are greater than 180°.
Simple polygons do not have their own sides. Complex polygons, also called self-intersecting polygons, have sides that intersect one another. A classic star is a complex polygon. Most people can quickly scribble a star on paper, but some refer to it as a pentagram, complex polygon, or self-intersecting polygon.
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Families of star-shaped complex polygons generally share common Greek numeral prefixes and use the suffix -gram: pentagram, hexagram, octagram, and so on.
You can’t draw a complex triangle. A complex polygon can be drawn for any polygon with four or more sides. A complex quadrilateral is the familiar bow tie shape, but is assumed to have only four sides since two opposite sides are twisted on top of each other.
Just as you don’t count the crossed sides as four line segments, you don’t count the two angles they form as interior angles either. A complex rectangle still has only four sides and four interior angles.
Complex polygons can be difficult to visualize unless you think of them as elastic. If you can lift and rotate part of the polygon so the two sides intersect and then lay it flat again, you end up with a complex polygon. Since you twisted two sides, you still have those two sides (their number does not double by crossing). Also, no new nodes are created where they cross.
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An unusually complex polygon is the antiparallelogram, which looks like a bird’s wing. An antiparallelogram (or crossed parallelogram) usually has two pairs of congruent, opposite sides, but one pair is crossed, forming what appears to be two triangles touching.
However, like any parallelogram, an antiparallelogram still only has four sides and four interior angles. However, its diagonals are outside the shape!
The interiors of all polygons can be divided into triangles. This is the easiest way to find the number of their interior angles. Take two less than the number of sides, n, and multiply by 180°: (n – 2) x 180°.
A circle is not a polygon, but an Ikosikaihenagon is a polygon. An Ikosikaihenagon is a 21-sided polygon. Most mathematicians and mathematics students simply write “21-Eck” in their name.
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Polygons can be examined and classified in many ways. Now you see that polygons can be regular or irregular, convex or concave, and simple or complex. If you see unusual polygons, you can determine their properties and classify them correctly.
To be a polygon, the shape must be flat and narrow in space, with only straight sides. polygons with congruent sides and common angles; all others are irregular. Polygons whose interior angles are all less than 180° are convex; If the polygon has at least one interior angle greater than 180°, it is concave. In geometry, a quadrilateral is a four-sided polygon with four sides (sides) and four vertices (corners). This word comes from the Latin word quadri, a variant of four, and latus, meaning side. It is also called quadrilateral, it comes from the Greek “tetra” meaning “four” and “gon” meaning “corner” or “corner”, by analogy with other polygons (e.g. ptagon). Since “gon” means “corner”, it is also called a square or 4-corner. A rectangle with points A, B, C, and D is sometimes dotted as ◻ A B C D.
A rectangle is either simple (does not intersect) or complex (intersects or intersects itself). A simple rectangle is either convex or concave.
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So the interior angles of a simple (and planar) rectangle ABCD add up to 360 degrees of arc
Types Of Quadrilaterals
This is a special case of the formula for the number of interior angles of an n-gon: S = (n − 2) × 180°.
In a convex quadrilateral, all interior angles are less than 180° and two diagonals lie inside the quadrilateral.
A hollow quadrilateral has an interior angle greater than 180° and one of the two diagonals lies outside the quadrilateral.
Rectangles that intersect are called various cross rectangles, cross rectangles, butterfly rectangles, or bow tie rectangles. In a crossed rectangle, the four “internal” angles on either side of the intersection (two acute and two reflections, all left or all right if the image is traced) add up to 720°.
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The two bimedians of a convex quadrilateral are the line segments connecting the midpoints of opposite sides.
They intersect at the ‘vertex’ of the quadrilateral (see § Exceptional point and line in lower convex quadrilateral).
Four angles of a convex quadrilateral are perpendicular to the side – through the midpoint of the opposite side.
There are several general formulas for the area K of a convex quadrilateral ABCD with sides a = AB, b = BC, c = CD and d = DA.
What Are The Types Of Quadrilaterals?
For orthodiagonal rectangles (e.g. rhombus, square and kite) this formula reduces to K = p q 2 }} since θ is 90°.
Where the sides are in the order a, b, c, d, where s is the semicircumference and A and C are two (actually two) opposite angles. This reduces to Brahmagupta’s formula for the area of a cyclic rectangle – wh A + C = 180°.
Another area formula in terms of sides and angles, where angle C is between sides b and c and A is between sides a and d is
In the case of a cyclic quadrilateral, the final formula is K = a d + b c 2 sin A . }Sin.}
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In a parallelogram where both pairs of sides and opposite angles are equal, this formula reduces to K = a b ⋅ sin A . .}
Alternatively, we can write the area in terms of the sides and the intersection angle θ of the diagonals, as long as θ is not 90°:
Where x is the distance between the centers of the diagonals and φ is the angle between the bimedians.
The final trigonometric area formula including sides a, b, c, d and angle α (between a and b) is:
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This can also be used for the area of a concave rectangle (with a concave part opposite angle α) simply by changing the first sign + to -.
The following two formulas express the area using the sides a, b, c and d, the semicircumference s and the diagonals p, q:
K = ( s − a ) ( s − b ) ( s − c ) ( s − d ) − 1 4 ( a c + b d + p q ) ( a c + b d − p q ) , }(ac+bd+pq)(ac +bd-pq)}}, }
The first is reduced to Brahmagupta’s formula in the case of the cyclic quadrilateral, since th pq = ac + bd.
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The area can also be expressed in terms of bimedian m, n and diagonals p, q:
K = ( m + n + p ) ( m + n − p ) ( m + n + q ) ( m + n − q ) 2 , }}, }
The area of rectangle ABCD can be calculated using vectors. Assume that the vectors AC and BD form a diagonal from A to C and from B to D. The area of the quadrilateral is th
This is half the size of the cross vector AC and BD. Expressing in two-dimensional Euclidean space the vector AC as a free vector in Cartesian space equal to (x1, y1) and BD as (x2, y2), this can be rewritten as:
Congruent And Similar Shapes
The following table lists whether the diagonals in some basic quadrilaterals bisect, whether their diagonals are perpendicular, and whether their diagonals are the same length.
Note 1: Most general trapezoids and isosceles trapezoids do not have perpendicular diagonals, but there are infinitely many (not similar)
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