Area of quadrilateral formula

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A quadrilateral, sometimes also known as a tetragon or quadrangle (Johnson 1929, p.61) is a four-sided A quadrilateral with two sides For a planar convex quadrilateral (left figure above), let the lengths of the sides be , , , and , the , and the and . The . An equation for the sum of the squares of side lengths is (2) where is the in the is the separation of centers. Given any five points in the plane in general position, four will form a convex quadrilateral. This result is a special case of the so-called There is a beautiful formula for the area of a planar convex quadrilateral in terms of the vectors corresponding to its two diagonals. Represent the sides of the quadrilateral by the vectors , , , and arranged such that and the diagonals by the vectors and arranged so that and . Then (9) (Bretschneider 1842; Strehlke 1842; Coolidge 1939; Beyer 1987, p.123). The centroid of the vertices of a quadrilateral occurs at the point of intersection of the and joining pairs of opposite connecting the midpoints of the diagonals and (Honsberger 1995, pp.39-40). The four Any non-self- There is a relationship between the six distances , , , , , and between the four points of a quadrilateral (Weinberg 1972): More things to try: • • • References Beyer, W.H. (Ed.). Bretschneider, C.A. "Untersuchung der trigonometrischen Relationen des geradlinigen Viereckes." Archiv der Math. 2, 225-261, 1842. Casey, J. Coolidge, J.L. "A Historically Interesting Formula for the Area of a Quadrilateral."...

Area Of Quadrilateral The area of quadrilateral is the region enclosed by sides of the quadrilateral. We have already acquainted with the term area. It is defined as the region occupied inside the boundary of a flat object or figure. The measurement is done in square units with the standard unit being square metres (m 2). We know that the polygon with four sides is called a quadrilateral. A quadrilateral can be a square, rectangle, rhombus, kite, parallelogram and trapezium. In this article, we are going to learn the general formula for the area of a quadrilateral with many solved examples. Table of Contents: • • • • • • • • • • • What is a Quadrilateral? A quadrilateral is a polygon with four sides. A quadrilateral is a closed two-dimensional figure formed by joining the four points among which three points are non-collinear points. A quadrilateral has four sides, four angles and four vertices. The sides of the quadrilateral may or may not be equal. Properties of Quadrilateral • Every quadrilateral has 4 vertices and 4 sides enclosing 4 angles. • The sum of its interior angles is 360 degrees. • A quadrilateral, in general, has sides of different lengths and angles of different measures. However, squares, rectangles, parallelograms, etc. are special Area of Quadrilateral Formula The formula for the area of quadrilateral can be found using different methods such as dividing the quadrilateral into two triangles, or by using Heron’s formula or by using sides of the quadril...

• • • • • • • What is Area of a Quadrilateral? A Measuring the area of a quadrilateral To evaluate the area of a quadrilateral, we divide it into two basic geometric figures, such as Calculating the area of a quadrilateral • Draw a diagonal AC connecting two opposite vertices of the quadrilateral ABCD. • Draw a perpendicular each from the other two vertices (B and D) on the diagonal AC. • The area of the quadrilateral will be: Area of quadrilateral ABCD = Area of △ABC + Area of △ADC So, area of quadrilateral ABCD = (½× AC × BE) + (½× AC × DF) We can calculate the area of different types of quadrilaterals by using the given formula. For the quadrilateral ABCD, if we use centimeter as the unit of measurement, the unit of measure for the area will be cm 2. Area of a Rhombus To find the area of a rhombus, we divide the quadrilateral into two equal isosceles triangles using the two diagonals. In the given rhombus ABCD, the point of intersection of these diagonals is E. Thus the area of the rhombus is: Area of rhombus ABCD = Area of △ABC + Area of △ADC ⟹ Area of rhombus ABCD = (½ x AC x BE) + (½ x AC x ED) ⟹ Area of rhombus ABCD = ½ x AC (BE + ED) ⟹ Area of rhombus ABCD = ½ x AC x BD Area of a Square Using this relationship we can also find the Area of square ABCD = Area of △ABC + Area of △BCD ⟹ Area of △ABC = ½ * AC * AB ⟹ Area of △ABC = ½ * AC * AC (as AC = AB) ⟹ Area of △ABC = ½ * AC2 Similarly, Area of △BCD = ½ * CD2 Since, AC = CD, Area of △BCD will be ½ * AC2 Thus, area of...

The height is perpendicular to the base, so you would have to extend the line segment of the base which is 4 at least to the point of vertex on top left. Then the same 5 on bottom would be the perpendicular distance to this vertex. Think of the two bases as being parallel, distance between them will remain constant. - [Instructor] What we're going to try to do in this video is find the area of this figure. And we can see it's a quadrilateral. It has 1, 2, 3, 4 sides. And we know that this side and this side that they're parallel to each other. You can see that they both form right angles with this dotted line. So pause this video and see if you can find the area. All right. Now, if you had a little bit of trouble with that I'll give you a hint. What if we were to take this quadrilateral and divide it into two triangles? So let me do this in a color that you are likely to see. So if I were to draw a line like this it now divides the quadrilateral into two triangles. If I were to take this triangle right over here I could take it out and reorient it, so it looks something like this, where the base has length 8, and then the height right over here, the height this has length 5. So that would be that triangle. And then, this triangle over here if you were to take it out and reorient it a little bit it could look like this, where the base is 4, and the triangle looks something like, looks something like this. So the base is 4, and then the height is going to be 5. So this heigh...

Application of Heron’s Formula in Finding Areas of Quadrilaterals In geometry, the shapes can be classified into two-dimensional shapes and three-dimensional shapes. 2D shapes are the plane figures, which are made up of two dimensions such as length and breadth, whereas 3D shapes are the solid figures, which are made up of three-dimensions such as length, breadth and height. We know that a triangle is a 2D shape, whose area can be determined by using the formula ½ × b × h, if base and height of the triangle are given. What if only the sides of a triangle are given? How to find the The solution to this is by applying Heron’s formula. One can find the area of a triangle using Heron’s formula, only if the side measurements are given. Now, let us have a quick recall about Heron’s formula. Heron’s Formula – Finding Area of a Triangle If a, b and c are the sides of a triangle, and s is the semiperimeter of a triangle, then the formula to find the area of triangle using Area of Triangle = √[s(s-a)(s-b)(s-c)] Square units. Note: s is the semiperimeter, which means half the perimeter of a triangle, and it is found using the formula: s = (a+b+c)/2. Application of Heron’s Formula in Finding Areas of Quadrilaterals Examples Heron’s formula is also applicable to find the area of a quadrilateral if the quadrilaterals are divided into triangular parts. Once the quadrilaterals are divided into triangular forms, apply Heron’s formula to find the area of individual tria...