Question

find the area the quadrilateral whose vertives taken in order are ( -4,-2 ),(-3,-5),(3,-2) and (2,3)​

Answer 1

Answer:

the coordinates are in order . so alternate coordinates form diagonals of quadrilateral. area of quadrilateral can be derived as the sum of areas of two triangles made by one of the diagonals. we take (-4,-2),(-3,-5),(3,-2) as coordinates of one triangle and (-4,-2),(3,-2),(2,3) as coordinates of other triangle.

area of quadrilateral =

| -4. -2. 1. |. |. -4. -2. 1. |

1/2. | -3. -5. 1 |. + 1/2. | 3. -2. 1. |

| 3. -2. 1. |. |. 2. 3. 1. |

| -4. -2. 1. |. |. -4. -2. 1. |

1/2. |. 1. -3. 0 |. + 1/2 |. 7. 0. 0. |

|. 7. 0. 0 |. |. 6. 5. 0 |

= (1/2)*[1(0-(-21)] + (1/2)*[1(35-0]

= 1/2[21 + 35]

= (1/2)*56

= 28 square unit