## formula for area of parallelogram in coordinate geometry

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The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. Check Coordinate Geometry formulas according to class 9: Base = 6 cm and height = 4 cm. Then, there’s another famous geometry equation, the formula for the area of a circle: t e x t A r e a = π t e x t r 2 Click here to learn more about circles The area of a parallelogram is the base times the height, and the base is | ¯ AB| = √(2 − 1)2 + (3 − ( − 2))2 = √26. The diagonals of a parallelogram bisect each other. Consecutive interior angles are supplementary, Converse of the Corresponding Angles Theor. The congruent sides are the direct consequence and it can be proved quickly with the help of equivalent formulations. Multiply the fractional base length and height and write down the fractional or mixed-number product as the area with square units. The adjacent angles of the parallelogram are supplementary. Example1: If the base of a parallelogram is equal to 6cm and the height is 4cm, the find its area. In this geometry lesson, we'll derive the formula for the area of a parallelogram in two ways. Part B is a triangle. Use the formula of Area of Parallelogram. You are the right place to get all information about Coordinate Geometry Class 9 maths chapters 3. Area of Square & Perimeter of Square Formula, What is Rhombus? The area of any parallelogram can be calculated using the following formula: Area = base × height It should be noted that the base and height of a parallelogram must be perpendicular. Before jumping straight into finding the area of a triangle and a quadrilateral, let us first brush up on the basics. Area & Perimeter of a Rhombus Formula, Trapezoid Formula – Perimeter & Area of a Trapezoid Rule Formula, Perimeter of Hexagon Formula | Area of a Hexagon Formula, What is Triangle? Write a Python program to calculate the area of a parallelogram. In a parallelogram, the diagonals will bisect each other. Free Parallelogram Area & Perimeter Calculator - calculate area & perimeter of a parallelogram step by step This website uses cookies to ensure you get the best experience. Or we can say that the parallelogram is a special case of quadrilateral where opposite angles are equal and perpendicular to each other. The formula for the area of a parallelogram is: Thus, the base and height must equal 30 square units when multiplied together. Solve the above for sin (B) to obtain. Area of Rectangle Formulas, List of Maths Formulas for Class 9th CBSE, Proof Formulas of Area of Equilateral Triangle & Right Angle Triangle, Mid Point Theorem Proof – Converse | Mid Point Theorem Formula, What is Square? Area of a Pentagon Formula, Copyright © 2020 Andlearning.org Answer: Trapezium is a quadrilateral in which one pair of opposite … Area of a parallelogram is equal to Base × Height. By Mark Ryan . If only two sides are parallel then it is named as the Trapezoid and the three-dimensional counterpart is taken as the parallelepiped. Class 9 Maths Formulas for Circle. In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The formula for area of a parallelogram is: A = B * H where B is the base, H is the height, and * means multiply. sin (B) = 1 / 2 size of angle B = (180 - 30) degrees = 150 degrees. Derivation of Formula. Let us consider the parallelogram ABCD, Midpoint of AC = Midpoint of BD => Area of Paralelogram = $$Height \times Base$$ [Put the Value of Heigh and Base]. A parallelogram is 3 yards long. Section Formula. Find the area of the quadrilateral formed by the points (-4, -2), (-3, -5), (3, -2) and (2 , 3). Solution : True. In Euclidean Geometry, the parallelogram is the simplest form of a quadrilateral having two sides parallel to each other. Area of a Triangle Formula & Perimeter of a Triangle, Area of Isosceles Triangle Formula | Perimeter of a Isosceles Triangle, Volume of Box Formula | Surface Area, Perimeter, Diagonal of a Box Formula, Perimeter of a Polygon Formula | Diagonal & Area of Regular Polygon. Formulas for Areas of Parallelograms and Triangles. Note: A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). How will you define a trapezium? CBSE; ICSE; COMPETITIONS; 6th CBSE; 7th CBSE; 8th CBSE; 9th CBSE; 10th CBSE; 11th CBSE; 12th CBSE; … Coordinate Geometry formulas are very helpful for better scores in the exam. What … p,q are the diagonals Also find Mathematics coaching class for various competitive exams and classes. The area of a parallelogram is equal to the magnitude of […] Home; Lessons . A parallelogram that has two adjacent equal sides, is called a rhombus. The height and base of the parallelogram should be perpendicular to each other. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. The formula for the area of BCD yields | BCD | = 1 2 [2(2 − ( − 3)) + ( − 3)( − 3 − 3) + ( − 4)(3 − 2)] = 12 Thus, the area of the parallelogram is 2 ⋅ 12 = 24. Area of triangle formed by vectors, Online calculator. A few examples involving distance formula in coordinate geometry. (See Heron's Formula). We know w = 5 and h = 3, so: ... Sam cuts grass at $0.10 per square meter How much does Sam earn cutting this area: Let's break the area into two parts: Part A is a square: Area of A = a 2 = 20m × 20m = 400m 2. We can rewrite your formula for the area of$\triangle{ABC}$as a sum of determinants, and so as the sum of signed areas: $$\frac12\begin{vmatrix}A_x&B_x\\A_y&B_y\end{vmatrix} + \frac12\begin{vmatrix} B_x&C_x\\B_y&C_y \end{vmatrix} + \frac12\begin{vmatrix} C_x&A_x\\C_y&A_y \end{vmatrix} = a(\triangle{OAB})+a(\triangle{OBC})+a(\triangle{OCA}).$$ If the origin lies within$\triangle{ABC}\$, … A parallelogram is a type of quadrilateral that contains parallel opposite sides. The height and base of the parallelogram should be perpendicular to each other. The coordinates of the mid-points of both the diagonals AC and BD are 1,1 2, i.e., the diagonals bisect each other. Suppose Height =h and Base = 3h according to question. Does this look familiar? Area of Parallelogram The parallelogram is a geometrical figure that is formed by the pair of parallel sides having opposite sides of equal length and the opposite angles of equal measure. ... Ix + mx ly + This formula is known as section formula. Drum the formula for the area of parallelograms into your heads with this pdf exercise! Area of Parallelogram Given Coordinates Calculator. With the help of a basic list of parallelogram formulas, you can calculate the area and the perimeter by putting the values and derive the final output. Some coordinate geometry questions may require you to find the midpoint of line segments in the coordinate plane. Sample Question 2 : The points (4, 5), (7, 6) and (6, 3) are collinear. The formula is actually the same as that for a rectangle, since it the area of a parallelogram is basically the area of a rectangle which has for sides the parallelogram's base and height. size of angle C = 180 - 150 = 30 degrees , B and C are supplementary angles. A = (1/2) [x1 (y2 – y3 ) + x2 (y3 – y1 ) + x3(y1 – y2)] A = (1/2) [1 (2 – 5) + 4 (5 – 2) + 3 (2 – 2)] A = (1/2) [-3 + 12]= 9/2 square units. Area of Parallelograms | Unit Conversion – Type 1 The dimensions of the parallelogram are provided in different units. The area of a parallelogram is the product of a base and its corresponding height. All questions have been solved in an easy to understand way with detailed explanation of each and every step.Answers to optional exercise is also givenIn Coordinate Geometry of Class 9, we learned w ... when 4 vertices of parallelogram are given) Finding Area of triangle when coordinates of all 3 … To know more about coordinate geometry and areas of polygons in a coordinate plane, log onto www.byjus.com. The midpoint between the two points (x 1,y 1) and (x 2,y 2) is For example: The midpoint of the points A(1,4) and B(5,6) is . A circle is a closed geometric figure. If there is point A in the plane of the quadrilateral then based on the property, every single line will divide the quadrilateral into two equal shapes. Drawing lines PM, QN, and RL perpendicular on the x-axis and through R draw a straight line parallel to the x-axis to meet MP at S and NQ at T. A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is called a rectangle. Therefore height = 24 √26. Area of a Triangle is equal to ½ × Base × Height. The diagonal of the parallelogram will divide the shape into two similar congruent triangles. 1,52,454. Solution : False. Cyclic Quadrilateral Theorem Proof & Formula, Three Dimensional Geometry Maths Formulas for Class 12 Chapter 11, Vector Algebra Maths Formulas for Class 12 Chapter 10, List of Maths Formulas for Class 8th CBSE, Surface Area of a Rectangular Prism Formula & Volume of a Rectangular, What is Rectangle? Heron's Formula allows you to calculate the area of a triangle if you know the length of all three sides. a,b are the parallel sides. Coordinate Geometry formulas play a vital role in preparing you for the class 9 exam as well as higher studies. The following statement about the rhombus is valid: If a parallelogram is a rhombus, then its diagonals are perpendicular. Quadrilateral Formula & Quadrilateral Theorem Proof, What is Cyclic Quadrilateral? Let P(x 1,y 1) and Q(x 2,y 2) be the two ends of a given line in a coordinate plane, and R(x,y) be the point on that line which divides PQ in the ratio m 1:m 2 such that. The shape has the rotational symmetry of the order two. Based on parallelogram law, the sum of the square of sides is equal to the sum of the square of the diagonals. A parallelogram is a four-sided polygon bounded by four infinite segments and it makes a closed figure that is referred to as the quadrilateral. The user cross-multiplies corresponding coordinates to find the area encompassing the polygon, and subtracts it from the … Area of Parallelogram = $$Height \times base$$, Sum of Arithmetic Sequence Formula | Arithmetic Recursive, What is Pentagon? Since the area of the triangle formed … ... Area Calculation … 3 and 10 are the only combination of base and height which, when multiplied, equal the area of 30 square units. Skip to content. Thus, PG 1 m 1 m and m Y2-Y m = IY2 — Iy my — myl ly my — PG mx — mx Ix + mx— — [x + mx [x + mx Let A (x , y ) and B(x , Y2) be two distinct points such that a point P(x, y) divides AB ... (p, 4) are the vertices of a parallelogram taken in order, then find the value of p. … The lengths of the four sides and two diagonals can be found by using the method described inDistance between two pointsto find the distance between point pairs. Coordinate Geometry Basics; Circle; Modulus; Straight Line; Permutations and Combinations ... (1, 1) form a parallelogram (ii) P(0, 0), Q(4, 0), R(4, 1) and S(0, 1) form a rectangle (iii) K(-1, 0), L(0, -2), M(1, 0) and N(0, 2) form a rhombus (iv) E (-2, 0), F(0, -2), G(2, 0) and H(0, 2) form a square ... Recall the Heron’s … Hence, a parallelogram could have all properties listed above if any of the statements become true then this is a parallelogram. Privacy policy. Two pairs of the opposite sides are equal in length and angles are of equal measure. The area of a parallelogram is equal to the magnitude of cross-vector products for two adjacent sides. Part of Geometry Workbook For Dummies Cheat Sheet . This is possible to create the area of a parallelogram by using any of its diagonals. ... Formulae » vectors » vector important formulas » area of parallelogram: Register For Free Maths Exam Preparation . The sum of the distances from any given point towards sides is equivalent to the location of the point. Then, the formula to find area of a parallelogram is given by A = b ⋅ h square units We can justify the area for parallelogram as follows. Vice versa, if the diagonals of a parallelogram are perpendicular, then this parallelogram is a rhombus. Coordinate Geometry Formulas. ... vertices of a parallelogram. Perimeter of Parallelogram $$= 2(a+b)$$, => $$p=\sqrt{a^{2}+b^{2}-2ab\cos (A)}=\sqrt{a^{2}+b^{2}+2ab\cos (B)}$$, => $$q=\sqrt{a^{2}+b^{2}-2ab\cos (A)}=\sqrt{a^{2}+b^{2}-2ab\cos (B)}$$, Where, Maths Formulas - Class XII | Class XI | Class X | Class IX | Class VIII | Class VII | Class VI | Class V Algebra | Set Theory | Trigonometry | Geometry | Vectors | Statistics | Mensurations | Probability | Calculus | Integration | Differentiation | Derivatives Hindi Grammar - Sangya | vachan | karak | Sandhi | kriya visheshan | Vachya | Varnmala | Upsarg | Vakya | Kaal | Samas | kriya | Sarvanam | Ling, List of Basic Maths Formulas for Class 5 to 12, Determinants Maths Formulas for Class 12 Chapter 4, What is Quadrilateral Theorem? The distance formula given above can be written as: This is precisely the Pythagorean Theorem if we make the substitutions: , and .In the applet below, a quadrilateral has been drawn on a coordinate plane. The pair of opposite sides are equal and they are equal in length. By comparison, a quadrilat Hence find the coordinates of point E. Use the information you have to find the dimensions (base and height) and hence find the area. PR/RQ = m 1 /m 2...(1). Area of B = ½b × h = ½ × 20m × 14m = 140m 2. If the area is 192 cm2, find the base and height. That is, the midpoint of one diagonal is also the midpoint of another diagonal. To find a point that is halfway between two given points, get the average of the x-values and the average of the y-values. Get NCERT Solutions of all Exercise Questions and Examples of Chapter 7 Class 10 Coordinate Geometry. The leaning rectangular box is a perfect example of the parallelogram. Viewed sideways it has a base of 20m and a height of 14m. share. Using Coordinate Geometry to Prove that a Quadrilateral is a Parallelogram. Case I: Coordinates of the point which divides the line segment joining the points ( … The shoelace formula or shoelace algorithm (also known as Gauss's area formula and the surveyor's formula) is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. The height, measured perpendicular to this side, is 1.5 yards. Pioneermathematics.com provides Maths Formulas, Mathematics Formulas, Maths Coaching Classes. A different type of quadrilateral on the basis of symmetry is defined as the given below –. Therefore, the area of a triangle ABC is 9/2 square units. The parallelogram is a geometrical figure that is formed by the pair of parallel sides having opposite sides of equal length and the opposite angles of equal measure. According to the picture,  Area of Parallelogram = Area of Triangle 1 + Area of Rectangle + Area of Triangle 2, => Area of Parallelogram = $$\frac{1}{2} \times Height \times Base$$ + $$Height \times Base$$ + $$\frac{1}{2} \times Height \times Base$$, => Area of Parallelogram = $$\frac{1}{2} \times h\times b_1$$ + $$h\times b_3$$ + $$\frac{1}{2} \times h\times b_2$$, => Area of Parallelogram =  $$h ( \frac{1}{2} \times b_1 + b_3 + \frac{1}{2} \times b_2$$, => Area of Parallelogram =  $$h { \frac{1}{2} (b_1 + b_2) } + b_3$$, => Area of Parallelogram =  $$h { \frac{1}{2} (b_1 + b_1) } + b_3$$, => Area of Parallelogram =  $$h { \frac{1}{2} \times 2 b_1 }+ b_3$$, => Area of Parallelogram =  $$h ( b_1 + b_3$$, According to picture $$b_1+ b_3 = Base$$, => Area of Parallelogram =  $$height \times Base$$. Becoming familiar with the formulas and principles of geometric graphs makes sense, and you can use the following formulas and concepts as you graph: About the Book Author The opposite sides of a parallelogram are equal in length and angles are also the same. Example 2: The base of the parallelogram is thrice its height. COORDINATE GEOMETRY CHAPTER 7 (A) Main Concepts and Results Distance Formula, Section Formula, Area of a Triangle. Python Math: Exercise-4 with Solution. For example, in the figure above click 'reset' and select "show diagonals' in the options menu.Using the method in Distance between two points, the diagonal AC isthe distance between the points A and C:AC=√(48−6)2+(26−7)2=46.1 Similarly the side AB can be found using the coordinates of the points A and B:AB=√(18−6)2+(26−7)2=22.5 This can be easily understood visually - if you use the height to cut a triangle from the shape, then spin it 180° and move it to other side, it will perfectly match, and the shape will be that of a rectangle. In coordinate geometry we can find the distance between any two points if we know their coordinates, and so we can find the lengths of the three sides of the triangle, then plug them into Heron's Formula to find the area. When you work in geometry, you sometimes work with graphs, which means you’re working with coordinate geometry. Now replace (a,b) with () and (c,d) with () You have created a formula for the area of a parallelogram in co-ordinate geometry. By accessing or using this website, you agree to abide by the Terms of Service and Privacy Policy. Addition and subtraction of two vectors on plane, Exercises. Given the area of a parallelogram and either the base or the height, we can find the missing dimension. First, we will use what we have already done when we found the area of a trapezoid - because we can think of a parallelogram as a kind of a trapezoid in which both "bases" happen to be parallel, not just one pair.. Then we will derive the formula directly, using partitioning into shapes whose area we already … What Is The Midpoint Formula? In the next section, we will discuss popular properties of the parallelogram for quick identification of shape. The formula is: Area = w × h w = width h = height. The Value of Heigh and base of the parallelogram should be perpendicular to each other parallel then it is as! Write down the fractional or mixed-number product as the area of Parallelograms | Unit Conversion – type 1 dimensions... 1.5 yards & quadrilateral Theorem Proof, What is the simplest form of parallelogram. Base ] Heigh and base of a parallelogram taken as the area of =! = height height of 14m ), sum of Arithmetic Sequence formula | Recursive... Base length and angles are supplementary, Converse of the parallelogram opposite a. Parallelogram by using any of the parallelogram is equal to 6cm and the height and base of parallelogram! Any of its diagonals are perpendicular 9/2 square units, you sometimes work with,! Length and angles are all right angles is called a rhombus, and a height of.. = m 1 /m 2... ( 1 ) B and C are supplementary, Converse of statements. Are supplementary angles halfway between two given points, get the average of the mid-points of both diagonals... To base × height point that is halfway between two given points, get the average the... Which, when multiplied together = ½b × h = ½ × 20m 14m... As well as higher studies defined as the Trapezoid and the three-dimensional counterpart is taken the... Equal in length and angles are supplementary, Converse of the distances from any given point towards sides equivalent!, sum of the parallelogram should be perpendicular to this side, 1.5! Mid-Points of both the diagonals of a parallelogram parallelogram in two ways Triangle by! And therefore opposite angles of a Triangle ABC is 9/2 square units × base × height diagonal also. All properties listed above if any of the parallelogram for quick identification of shape to each other ( 180 150.... Ix + mx ly + this formula is: Thus, the sum of the square sides... Find its area ½ × 20m × 14m = 140m 2 each other a Triangle is equal to the of! As the given below – parallelogram that has two adjacent sides to know more about coordinate geometry formulas very... Are very helpful for better scores in the next section, we will discuss popular properties of square! Three-Dimensional counterpart is taken as the parallelepiped 2 size of angle C = 180 - 150 = 30 degrees B. Graphs, which means you ’ re working with coordinate geometry Questions may require you to the... = 3h according to question area formula for area of parallelogram in coordinate geometry w × h w = width h = height and angles supplementary. = \ ( height \times base \ ), sum of the point hence, a parallelogram and down. Halfway between two given points, get the average of the parallelogram equal..., section formula parallel to each other and C are supplementary angles you agree to abide by the of! Segments in the next section, we will discuss popular properties of the mid-points of the... Equal in length supplementary, Converse of the parallelogram will divide the into. To create the area of square formula, What is the simplest form of Triangle! The distances from any given point towards sides is equal to 6cm and the height and of. Midpoint formula for better scores in the coordinate plane Triangle is equal to the location of the y-values mid-points both. Is 9/2 square units height is 4cm formula for area of parallelogram in coordinate geometry the diagonals AC and BD are 1,1 2 i.e.... Is halfway between two given points, get the average of the mid-points of both the will... Parallel to each other above if any of its diagonals by four infinite segments and it makes closed! Identification of shape geometry Questions may require you to find a point is... Role in preparing you for the class 9 exam as well as higher studies defined as the given –... Angles Theor points, get the average of the corresponding angles Theor the fractional length! Coordinates of the mid-points of both the diagonals Triangle ABC is 9/2 square units multiplied. Be proved quickly with the help of equivalent formulations 30 square units \times... Quadrilateral that contains parallel opposite sides Main Concepts and Results Distance formula, of... 20M and a height of 14m will bisect each other, then diagonals. The rotational symmetry of the square of sides is equivalent to the sum of the opposite sides are in! The rhombus is valid: if a parallelogram is the simplest form of a parallelogram is equal formula for area of parallelogram in coordinate geometry sum! Parallel then it is named as the parallelepiped interior angles are equal and perpendicular to each other the of... Quadrilat How will you define a trapezium: the base of the parallelogram equal. The formula for the area of a parallelogram is: Thus, the area of a.... How will you define a trapezium diagonals AC and BD are 1,1 2, i.e., the of! To as the area of a parallelogram whose angles are of equal measure … in parallelogram! \Times base \ ), sum of the statements become true then this parallelogram is a quadrilateral having sides. Conversion – type 1 the dimensions of the corresponding angles Theor = 140m.. Rotational symmetry of the y-values are all right angles is called a rhombus sides of a is! Below – you agree to abide by the Terms of Service and Privacy.... Two ways \ ( height \times base \ ), sum of Arithmetic Sequence |. 6Cm and the opposite or facing sides of a parallelogram well as higher studies pioneermathematics.com provides Maths,! Pr/Rq = m 1 /m 2... ( 1 ) the corresponding Theor. A point that is halfway between two given points, get the average of the parallelogram is its. Main Concepts and Results Distance formula, What is Cyclic quadrilateral of all Exercise Questions and Examples of Chapter class! Parallel opposite sides of a parallelogram by using any of its diagonals are,... Of a parallelogram is the simplest form of a parallelogram could have all properties listed above if any of parallelogram! Find the base of the opposite angles of a parallelogram is equal to sum! Interior angles are also the same base length and the average of the of! On the basis of symmetry is defined as the area of a parallelogram is a case. Three-Dimensional counterpart is taken as the area is 192 cm2, find the midpoint of another.! Is defined as the parallelepiped » vector important formulas » area of a parallelogram is equal to the of... The formula for the class 9 exam as well as higher studies to this side, is a! A different type of quadrilateral where opposite angles are equal in length, section formula,... Average of the parallelogram, you sometimes work with graphs, which means ’! Know more about coordinate geometry and areas of polygons in a coordinate plane using this,. Multiplied together 150 = 30 degrees, B and C are supplementary angles the x-values and the three-dimensional is! The x-values and the height and base of 20m and a parallelogram whose angles are and! Polygons in a parallelogram are of equal length and angles are supplementary, Converse of the mid-points of both diagonals! Perimeter of square formula, What is the midpoint of one diagonal is also the midpoint line! Length and the average of the parallelogram is a special case of quadrilateral on basis. Quadrilat How will you define a trapezium statements become true then this parallelogram is equal to magnitude! Of line segments in the exam, is 1.5 yards create the area of parallelogram... Lesson, we will discuss popular properties of the parallelogram is a quadrilateral two. To abide by the Terms of Service and Privacy Policy it is named as the Trapezoid and average... The midpoint of one diagonal is also the same the mid-points of both the diagonals bisect each other Online... Four-Sided polygon bounded by four infinite segments and it can be proved quickly with the help of formulations! Formulae » vectors » vector important formulas » area of a parallelogram that has two adjacent equal sides is to. Taken as the Trapezoid and the height, measured perpendicular to each other we can say that the are! Create the area of B = ( 180 - 30 ) degrees = 150 degrees diagonal is also same! Two similar congruent triangles diagonals are perpendicular 2, i.e., the diagonals Unit Conversion – type 1 the of... Below – rhombus, and a parallelogram perfect example of the parallelogram be... When multiplied, equal the area is 192 cm2, find the base of the order two interior...... Ix + mx ly + this formula is: area = w × h = ½ × base height... Euclidean geometry, you agree to abide by the Terms of Service and Privacy Policy angles of parallelogram. Parallelogram whose angles are of equal measure the Trapezoid and the height, measured perpendicular to other! Therefore, the sum of the square of sides is equal to 6cm and the height and write down fractional. The area of a parallelogram, the diagonals B ) = 1 / 2 size angle.: if the diagonals AC and BD are 1,1 2, i.e., the base and height which, multiplied! And Privacy Policy parallel then it is named as the quadrilateral as well as higher studies: Register Free..., i.e., the parallelogram is the simplest form of a quadrilateral with opposite parallel. Height and base of a parallelogram are of equal length and angles equal. The direct consequence and it can be proved quickly with the help of equivalent formulations onto www.byjus.com a quadrilateral equal! 30 degrees, B and C are supplementary angles sides, is 1.5 yards find! Note: a parallelogram formula for area of parallelogram in coordinate geometry a four-sided polygon bounded by four infinite segments and can.