Let P(−5,−3); Q(−4,−6); R(2,−3) and S(1,2) be the vertices of quadrilateral PQRS.

Area of the quadrilateral PQRS = Area of ∆PQR + Area of ∆PSR

Area of the triangle having vertices (x₁,y₁), (x₂,y₂) and (x₃,y₃)

= |x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)|

Area of ∆PQR = |− 5( − 6 + 3 ) − 4( − 3 + 3 ) + 2( −3 + 6) |

= |15 + 0 + 6|

= sq. units

Area of ∆PSR = | − 5( 2 + 3 ) + 1( − 3 + 3 ) + 2( − 3 − 2) |

= | − 25 + 0 – 10 |

= sq. units

Area of the quadrilateral PQRS = + = 28 sq. units

∴Hence, the area of the quadrilateral is 28 sq. units.

(given answer is wrong, its not 13, it is 28 )