Area of Quadrilateral

It is not a quadrilateral Introduction A quadrilateral is a closed figure bounded by four line segments such that no two line segments cross each other. It is a quadrilateral It is not a quadrilateral

Quadrilateral Properties Corner2 Corner1 Side 1 ∠1 ∠2 Side 4 Side 2 ∠3 ∠4 Side 3 Corner3 Corner4 A quadrilateral has: four sides (edges) four vertices (corners) interior angles that add to 360 degrees: ∠1 + ∠2 + ∠3 + ∠4 = 360

Types of Quadrilateral 2 opposite sides are parallel Only 1 opposite sides are parallel Parallelogram Trapezium 2 opposite sides are equal and all interior angle are 900 All sides are equal and all interior angle are 900 Trapezium with non parallel sides are equal Isoceles Trapezium Rectangle Square

Formula for finding the area of Quadrilateral In a quadrilateral ABCD, draw the diagonal AC. It divides the quadrilateral into two triangles ABC Draw altitudes BF and DE to the common base AC. and ADC. Area of the quadrilateral ABCD= Area of ∆ABC + Area of ∆ADC = x AC x h1 + x AC x h2 = x AC x [h1 + h2] = x d x [h1 + h2] Where d = length of the diagonal AC and h1 and h2 are perpendiculars drawn to the diagonal from the opposite vertices. Area of the quadrilateral ABCD = x d x [h1 + h2] sq.units

Area of Quadrilateral = 100 cm2 Example 1: Calculate the area of a quadrilateral PQRS shown in the figure Solution: Given: d = 10 cm ,h1 = 8 cm , h2 = 12 cm Area of a quadrilateral PQRS = x d x [h1 + h2] = x 10 x [8 + 12] = x 10 x 20 = 5 x 20 ` = 100 cm2 5 Area of Quadrilateral = 100 cm2

Area of a quadrilateral = 32.4 cm2 Example 2: Find the area of the quadrilateral whose diagonal and heights are: d = 3.6 cm, h1 = 8 cm, h2 = 10 cm Solution: Given: h1 = 8 cm , h2 = 10 cm , d = 3.6 cm Area of a quadrilateral = x d x [h1 + h2] = x 3.6 x [8 + 10] = x 3.6 x 18 = 3.6 x 9 = 32.4 cm2 9 Area of a quadrilateral = 32.4 cm2

Try these 1. Calculate the area of a quadrilateral ABCD 2. Find the area of quadrilateral whose diagonal is 9m and h1=5m and h2=3m