Question

Find the area of quadrilateral whose vertices are (–5, 7), (–4, –5), (–1, –6) and (4, 5)​

Answer 1

72sq units is the right answer

Answer 2

Given : A quadrilateral whose vertices are (–5, 7), (–4, –5), (–1, –6) and (4, 5)​

To find :   area of quadrilateral

Solution:

quadrilateral vertices are (–5, 7), (–4, –5), (–1, –6) and (4, 5)​

Lets break Quadrilateral into two triangles

(–5, 7), (–4, –5)(–1, –6)   &  (–5, 7), ( 4,  5)(–1, –6)

Area of Triangle

(–5, 7), (–4, –5)(–1, –6)

= (1/2) |  -5 ( -5 -(-6)) -4(-6 -7)  - 1(7 -(-5))|

= (1/2) | -5(1)  - 4(-13) -1(12) |

= (1/2) | -5 + 52 - 12 |

= (1/2) | 35  |

= 35/2

Area of Triangle

(–5, 7), (4, 5)(–1, –6)

= (1/2) |  -5 ( 5 -(-6)) +4(-6 -7)  - 1(7 - 5))|

= (1/2) | -5(11)  + 4(-13) -1( 2) |

= (1/2) | -55 - 52 -  2 |

= (1/2) | -109  |

= 109/2

Area of Quadrilateral = 35/2 + 109/2

= 144/2

= 72

Area of Quadrilateral =  72 sq units

Learn more:

Find the area of quadrilateral whose vertices are A(0,-4),B(4,0),C(-4 ...

https://brainly.in/question/12358129

Find the area of the quadrilateral whose vertices are a(0 0) b(6 0) c ...

https://brainly.in/question/5528711

Find the area of the quadrilateral whose vertices are at (9,-2), (-8,-4 ...

https://brainly.in/question/12015497