Question

if A (-5,7),B (-4,-5) ,C (-1,6) and D (4,2) are the vertices of a quadrilateral , find the area of quadrilateral ABCD

Answer 1

HELLO DEAR,

A(-5,7), B(-4,-5) , C(-1,6) and D(4,2)

area of triangle ABC= 1/2[(-5)(-5-6) + (-4)(6-7) +(-1)(7+5) ]

=> 1/2[(-5 × -11) + ( -4 × -1) + (-1 × 12)]

=> 1/2[ (55 + 4 - 12]

=> 1/2[59 - 12]

=> 1/2[47]

=> 47/2unit²


area of ∆BCD = 1/2[(-5)(-6 - 2) + (-1) (2 - 7) + (4)(7 - 6)]

=> 1/2[(-5 × -8 ) + (-1 × -5) + (4 × 1)]

=> 1/2[ 40 + 5 + 4]

=> 1/2(49)

=> 49/2unit²

Area of quadrilateral = ara.ABC + areaBCD

=> 47/2 + 49/2

=> (47 + 49)/2

=> (96)/2

=> 48unit²


I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

heya..!!!



we know that

area of triangle = 1/2[(x1)(y2 - y3) + (x2)(y3 - y1) + (x3)(y1 - y2)]

A(-5,7), B(-4,-5) , C(-1,6) and D(4,2) 

in ∆ ABC
x1 = -5 , x2 = -4 ,x3 = -1
Y1 = 7 , Y2 = -5 , Y3 = 6

area of triangle ABC= 1/2[(-5)(-5-6) + (-4)(6-7) +(-1)(7+5) ]

=> 1/2[(-5 × -11) + ( -4 × -1) + (-1 × 12)]

=> 1/2[ (55 + 4 - 12]

=> 1/2[59 - 12]

=> 1/2[47]

=> 47/2unit²


IN ∆ BCD
X1 = -5 , x2 = -4 , x3 = 4
y1 = 7 , y2 = -5 , y3 = 2

area of ∆BCD = 1/2[(-5)(-6 - 2) + (-1) (2 - 7) + (4)(7 - 6)]

=> 1/2[(-5 × -8 ) + (-1 × -5) + (4 × 1)]

=> 1/2[ 40 + 5 + 4]

=> 1/2(49)

=> 49/2unit²

Area of quadrilateral = area(ABC) + area(BCD)

=> 47/2 + 49/2

=> (47 + 49)/2

=> (96)/2

=> 48unit²