1. Area of Quadrilateral

2. 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

3. 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

4. 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

5. 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 h 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

6. 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 [ ]
= x 10 x 20
= 5 x 20
` = cm2 5
Area of Quadrilateral = 100 cm2

7. 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 x [ ]
= x x 18
= 3.6 x 9 = 32.4 cm2 9
Area of a quadrilateral = 32.4 cm2

8. 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