# FIND AREA OF QUADRILATERAL WITH VERTICES

Find Area of Quadrilateral with Vertices :

In this section, we will learn, how to how to find area of a quadrilateral with vertices.

## How to Find Area of Quadrilateral with Coordinates

To find the area of the quadrilateral with the given four vertices, we may use the formula given below.  ## Find Area of Quadrilateral with Vertices - Practice Questions

Question 1 :

Find the area of the quadrilateral whose vertices are at

(i) (–9, –2), (–8, –4), (2, 2) and (1, –3)

Solution : By taking the points in counter clock wise, we have to find the area of CABD. =  (1/2)[(-4 + 36 + 24 + 2) - (-18 + 16 - 4 - 6)]

=  (1/2)[(62-4) - (-28 + 16)]

=  (1/2)[58 - (-12)]

=  (1/2)(58 + 12)

=  (1/2)(70)

=  35 square units.

(ii) (–9, 0), (–8, 6), (–1, –2) and (–6, –3)

Solution :

By plotting the given points in the graph paper, we get By taking the points in counter clock wise direction, we find the area of BADC. =  (1/2)[(0 + 27 + 12 - 6) - (-54 + 0 + 3 + 16)]

=  (1/2)[(39 - 6) - (-54 + 19)]

=  (1/2)[(33) - (-35)]

=  (1/2)(33 + 35)

=  (1/2) (68)

=  34 square units.

Question 2 :

Find the value of k, if the area of a quadrilateral is 28 sq.units, whose vertices are (–4, –2), (–3, k), (3, –2) and (2, 3)

Solution :

Area of quadrilateral  =  28 square units [(-4k  + 6 + 9 - 4) - (6 + 3k - 4 - 12)]  =  28(2)

(-4k + 11) - (3k - 10)  =  56

-4k + 11 - 3k + 10  =  56

-7k  =  56-21

-7k  =  35

k  =  35/(-7)

k  =  -5

Hence the value of k is -5.

Question 3 :

If the points A(-3, 9) , B(a, b) and C(4, -5) are collinear and if a + b = 1 , then find a and b.

Solution : [(-3b - 5a + 36) - (9a + 4b + 15)]  =  0

-3b - 5a + 36 - 9a - 4b - 15  =  0

-5a - 9a - 3b - 4b + 21  =  0

-14a - 7b + 21  =  0

2a + b  =  3

2a + b  =  3  -----(1)

a + b  =  1  -----(2)   (Given)

(1) - (2)

2a + b - (a + b)  =  3 - 1

2a - a + b - b  =  2

a  =  2

By applying the value of a in (2), we get

2 + b  =  1

b  =  -1 After having gone through the stuff given above, we hope that the students would have understood, how to find area of quadrilateral with vertices.

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