# Find the area of the quadrilateral whose vertices, taken in order, are (- 4, - 2), (- 3, - 5), (3, - 2) and (2, 3)

**Solution:**

Let ABC be any triangle whose vertices are A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃).

Then, Area of a triangle is given by 1/2 [x₁ (y₂ - y₃) + x₂ (y₃- y₁) + x₃ (y₁ - y₂)] ------ (1)

Let the vertices of the quadrilateral be A (- 4, - 2), B (- 3, - 5), C (3, - 2), and D (2, 3)

Join AC to form two triangles ∆ABC and ∆ACD.

We know that, area of a triangle = 1/2 [x₁ (y₂ - y₃) + x₂ (y₃- y₁) + x₃ (y₁ - y₂)]

By substituting the values of vertices, A, B, C in the formula.

Area of ΔABC = 1/2 [(- 4){(- 5) - (- 2)} + (- 3){(- 2) - (- 2)} + 3{(- 2) - (- 5)}]

= 1/2 (12 + 0 + 9)

= 21/2 square units

By substituting the values of vertices, A, C, D in the Equation (1),

Area of ΔACD = 1/2 [(- 4){(- 2) - 3} + 3{(3) - (- 2)} + 2{(- 2) - (- 2)}]

= 1/2 (20 + 15 + 0)

= 35/2 square units

Area of ABCD = Area of ΔABC + Area of ΔACD

= (21/2 + 35/2) square units

= 28 square units

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 7

**Video Solution:**

## Find the area of the quadrilateral whose vertices, taken in order, are (- 4, - 2), (- 3, - 5), (3, - 2) and (2, 3)

NCERT Class 10 Maths Solutions - Chapter 7 Exercise 7.3 Question 4

**Summary:**

The area of the quadrilateral whose vertices, taken in order, are (- 4, - 2), (- 3, - 5), (3, - 2) and (2, 3) is 28 square units.

**☛ Related Questions:**

- Find the area of the triangle whose vertices are:(i) (2, 3), (- 1, 0), (2, - 4)(ii) (- 5, - 1), (3, - 5), (5, 2)
- In each of the following find the value of ‘k’, for which the points are collinear.(i) (7, - 2), (5, 1), (3, k)(ii) (8, 1), (k, - 4), (2, - 5)
- Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, - 1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.
- You have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. Verify this result for ∆ABC whose vertices are A (4, - 6), B (3, - 2) and C (5, 2)

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