The area of a quadrilateral can be determined when the coordinates of vertices of the quadrilateral are given. √(s 1 - p) (s 1 - q) (s 1 - r) (s 1-s) - pqrs cos²(θ /2).Īrea of a Quadrilateral using Coordinate Geometry Now apply the Bretschneider’s formula as follows:.Find the semi-perimeter of the quadrilateral.Steps to find the area of a quadrilateral using the Bretschneider’s formula are as follows: The opposite angles ∠A and ∠C are denoted as θ 1 and θ 2 respectively. Consider the quadrilateral ABCD with lengths of sides as p,q,r, and s. ⇒ Area of ?ABCD = Īrea of a Quadrilateral using Bretschneider’s FormulaĪrea of a quadrilateral can be determined when the lengths of the sides and the opposite angles are given using the Bretschneider’s formula. The area of the quadrilateral ABCD = area of ΔABC area of ΔADC.Find the semi-perimeter of the ΔABC and ΔADC.Steps to find the area of the quadrilateral with the above information: Let AB = a, BC = b, CD = c, DA = d and AC = e. Here the length of the diagonal AC and the lengths of the sides are given. The diagonal AC divides the quadrilateral into two triangles. In such situations, the Heron’s formula should be used.Ĭonsider a quadrilateral ABCD with a diagonal AC. Sometimes, the lengths of the four sides of the quadrilateral and the length of the diagonal are given. However, in some situations, these details are not available. (½) × Length of the diagonal × (sum of the heights of the triangles) provided the length of a diagonal and heights are given.Īrea of a Quadrilateral using Heron’s FormulaĪrea of a quadrilateral can be determined by splitting the quadrilateral into two triangles when the length of the diagonal and heights of the triangles are provided. Therefore we can infer that area of a quadrilateral can be obtained by using the below formula ⇒ Area of \(\Box\)ABCD = Area of ΔADC Area of ΔABC The area of the quadrilateral can be determined by adding the areas of the two triangles ΔADC and ΔABC. The heights of the two triangles are h1 and h2 respectively. The quadrilateral ABCD is divided into two triangles namely ΔADC and ΔABC. In the \(\Box\)ABCD, let the diagonal of the quadrilateral be denoted by ‘d’. Let us consider the following example to get a clear idea. In this method, the area of the two triangles are calculated separately and then the two areas are summed up to obtain the area of the quadrilateral. If the length of the diagonal and the heights of the two triangles are known then it is the best method to use for finding the area of the quadrilateral. The area of a quadrilateral can be measured by splitting it into two triangles. The area of a general quadrilateral can be determined using Heron’s formula or Bretschneider’s formula or splitting the quadrilateral into two triangles or by using coordinate geometry.Īrea of a Quadrilateral by Splitting it into Two Triangles However, for finding the area of a general quadrilateral, there are different methods that can be followed. However, the method or formula to be applied for finding the area of a quadrilateral must be determined based on the information provided and the type of the quadrilateral.įor finding the area of a quadrilateral like square, rectangle, parallelogram, and rhombus, it is always advisable to apply the respective formulas directly. The area of a quadrilateral like square, rectangle, or parallelogram can be calculated by directly using the formulas. Several methods are used to measure the area of a quadrilateral. Any value depicting the area of a surface is denoted using the units like m², cm², sq. Area is calculated for two-dimensional shapes and it is measured in square units. The area of a quadrilateral can be defined as the amount of space enclosed within the sides of a quadrilateral. Since square and rhombus have sides that are equal in length, they are called regular quadrilaterals while the rest are irregular quadrilaterals. The six types of quadrilaterals are as follows: Quadrilaterals are broadly classified into six types based on their properties. If the sides of the quadrilateral are not equal, then it is said to be an irregular quadrilateral. If all the four sides of the quadrilateral are equal, then it is said to be a regular quadrilateral. There can be only two diagonals in a quadrilateral.Ī quadrilateral may be classified as regular or irregular depending on the sides of the polygon.The sum of the four angles of a quadrilateral must be equal to 360 o.A quadrilateral must have four sides, four vertices, and four angles.Some of the properties of a quadrilateral are as follows: In short, a quadrilateral is a four-sided closed polygon. A Quadrilateral can be defined as a closed polygon enclosed by four equal or unequal sides.
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