Area of quadrilateral in coordinate geometry

• Courses • Online Coding Classes For Kids • Online Chess Classes For Kids • Web & Mobile App Development Course For Kids • Artificial Intelligence Coding Course For Kids • Design Course For Kids • Online Drawing & Animation Classes For Kids • Maths Course For Kids • Sample Papers • Class 4 Maths Sample Paper • Class 5 Maths Question Paper • Class 6 Maths Question Papers • Class 7 Maths Sample Paper • Class 8th Maths Sample Papers • Class 9 Maths Sample Paper • Class 10 Maths Sample Paper • Blog • Reviews • English • हिन्दी Table of Contents • • • • • • • • • This post is also available in: हिन्दी (Hindi ) A In this article, you will learn how to find the area of an irregular quadrilateral (or any type of quadrilateral) using coordinate geometry. Area of Quadrilateral in Coordinate Geometry When a diagonal is drawn in a quadrilateral it is divided into two triangles. The area of the quadrilateral will be equal to the sum of the areas of these two triangles. To find the area of a quadrilateral, we find the area of individual triangles and add their areas. In the above figure, quadrilateral $\text(5,4)$, in that sequence. • Determine the area of the quadrilateral with the following vertices $(7, 5)$, $(4, 10)$, $(-6, 11)$, and $(-5,2)$. • Find the area of the quadrilaterals, the coordinates of whose vertices are $(1,2)$, $(6,2)$, $(5,3)$, and $(3,4)$. • Find the area of the quadrilateral, the coordinates of whose angular points are taken in order are ...

What is the area in square units, of a quadrilateral whose vertices are $$(5,3), (6,-4), (-3,-2), (-4,7)?$$ I have tried creating the triangles, but didn't know how to find the diagonal. I wanted to try the shoelace method but I thought it only worked for triangles. The answer that was provided is $69$. There's a neat method we can use in this case called the Application of this formula gives us that the area is $$\begin$$ Let $A(5,3), B(6,-4), C(-3,-2), D(-4,7)$. The area of $\triangle ABC$ is given by $$\frac.$$ You want a really easy way to do this?? Check this out! Given the four vertices: (5,3),(6,−4),(−3,−2),(−4,7), find the Area: (1) Determine the diagonal "vectors" (by subtracting the opposite vertices): d1 = (5, 3) - (-3,-2) = (8, 5) d2 = (6,-4) - (-4, 7) = (10,-11) (2) The area equals 1/2 of the absolute value of the "cross-product" of the diagonals: X = 1/2 * | (8 * -11) - (10 * 5) | = 1/2 * 138 = 69. This works for any irregular quadrilateral.

Area of a Quadrilateral If ABCD is a quadrilateral, then considering the diagonal AC, we can split the quadrilateral ABCD into two triangles ABC and ACD. Using area of triangle formula given its vertices, we can calculate the areas of triangles ABC and ACD. Now, Area of the quadrilateral ABCD = Area of triangle ABC + Area of triangle ACD We use this information to find area of a quadrilateral when its vertices are given. Let A( x 1, y 1), B( x 2, y 2), C( x 3, y 3) and D( x 4, y 4) be the vertices of a quadrilateral ABCD. Now, Area of quadrilateral ABCD = Area of the ΔABD + Area of the ΔBCD (Fig5.9) Thinking Corner : How many triangles exist, whose area is zero? The following pictorial representation helps us to write the above formula very easily. Take the vertices A( x 1, y 1), B( x 2, y 2), C( x 3, y 3) and D( x 4, y 4) in counter-clockwise direction and write them column-wise as that of the area of a triangle. Therefore, area of the quadrilateral ABCD = 1/2 sq.units. Note · To find the area of a quadrilateral, we divide it into triangular regions, which have no common area and then add the area of these regions. · The area of the quadrilateral is never negative. That is, we always take the area of quadrilateral as positive. Thinking Corner: If the area of a quadrilateral formed by the points ( a, a), (– a, a), ( a, – a) and (– a, – a), where a ≠ 0 is 64 square units, then identify the type of the quadrilateral Find all possible values of a. • Prev Page •

\( \newcommand\) • • • • • • • • Identify and calculate area of shapes based on coordinates on a plane. Quadrilateral Classification What if you were given a quadrilateral in the coordinate plane? How could you determine if that quadrilateral qualifies as one of the special quadrilaterals: parallelograms, squares, rectangles, rhombuses, kites, or trapezoids? When working in the coordinate plane, you will sometimes want to know what type of shape a given shape is. You should easily be able to tell that it is a quadrilateral if it has four sides. But how can you classify it beyond that? First you should graph the shape if it has not already been graphed. Look at it and see if it looks like any special quadrilateral. Do the sides appear to be congruent? Do they meet at right angles? This will give you a place to start. Once you have a guess for what type of quadrilateral it is, your job is to prove your guess. To prove that a quadrilateral is a parallelogram, rectangle, rhombus, square, kite or trapezoid, you must show that it meets the definition of that shape OR that it has properties that only that shape has. If it turns out that your guess was wrong because the shape does not fulfill the necessary properties, you can guess again. If it appears to be no type of special quadrilateral then it is simply a quadrilateral. The examples below will help you to see what this process might look like. Classifying Parallelograms Determine what type of parallelogram TUNE is: \(T(0,10),...

A ( − 5 , − 5 ) A(-5,-5) A ( − 5 , − 5 ) A, left parenthesis, minus, 5, comma, minus, 5, right parenthesis , B ( − 4 , − 6 ) B(-4,-6) B ( − 4 , − 6 ) B, left parenthesis, minus, 4, comma, minus, 6, right parenthesis , C ( 2 , − 3 ) C(2,-3) C ( 2 , − 3 ) C, left parenthesis, 2, comma, minus, 3, right parenthesis , and D ( 1 , 2 ) D(1,2) D ( 1 , 2 ) D, left parenthesis, 1, comma, 2, right parenthesis are the vertices of a quadrilateral A B C D ABCD A B C D A, B, C, D . • Your answer should be • an integer, like 6 6 6 6 • a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5 • a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4 • a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4 • an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75 • a multiple of pi, like 12 pi 12\ \text 2 / 3 pi 2, slash, 3, space, start text, p, i, end text sq. units