Question

If (-1, -1), (5,-2), (6, 1) and (2, 3) taken in order are the
coordinates of the vertices of a quadrilateral, then the area
enclosed is
45 sq. units
30 sq, units
22.5 sq, units
20.5 sq, units

Answer 1

Answer:

your answer :-. 20.5 sq. units

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Answer 2

Given : (-1, -1), (5,-2), (6, 1) and (2, 3) taken in order are the  coordinates of the vertices of a quadrilateral,  

To Find : the area  enclosed

Solution:

Let say

P (-1, -1), Q (5,-2),   R  (6, 1) and S (2, 3)

Area pf PQRS = Area of ΔPQR + Area of ΔPSR

Area of ΔPQR  

P (-1, -1), Q (5,-2),   R  (6, 1)

= (1/2) |  -1 (-2 - 1) + 5(1-(-1))  + 6(-1-(-2))|

= (1/2) |  3 + 10 + 6 |

= 19/2

Area of ΔPSR  

P (-1, -1),  S (2, 3),   R  (6, 1)

= (1/2) |  -1 (3 - 1) + 2(1-(-1))  + 6(-1-3)|

= (1/2) |  -2 + 4 - 24 |

= (1/2) | - 22 |

= 22/2

= 11

19/2  + 11

= 41/2  sq units

= 20.5 sq units

area   enclosed is  20.5 sq units

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