Question

If A(–5, 7), B(–4, –5), C(–1, –6) and D(4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD

Answer 1

Answer

Joining BD, there are two triangles.

Area of quad ABCD = Ar △ABD + Ar △BCD

Ar △ABD = ½| (-5)(-5 - 5) + (-4)(5 - 7) + (4)(7 + 5) |

= 53 sq units

Ar △BCD = ½| (-4)(-6 - 5) + (-1)(5 + 5) + (4)(-5 + 6) |

= 19 sq units

Hence, area of quad ABCD = 53 + 19 = 72 sq units

Answer 2

Joining BD, there are two triangles.

Area of quad ABCD = Ar △ABD + Ar △BCD

Ar △ABD = ½| (-5)(-5 - 5) + (-4)(5 - 7) + (4)(7 + 5) |

= 53 sq units

Ar △BCD = ½| (-4)(-6 - 5) + (-1)(5 + 5) + (4)(-5 + 6) |

= 19 sq units

Hence, area of quad ABCD = 53 + 19 = 72 sq units

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