Question

Find the area of quadrilateral whose vertices are (-4,5)(0,7)(5,-5)(-4,-2)​

Answer 1

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Explanation:

Given :

Vertices of a Quadrilateral are :A(-4,5),B(0,7),C(5,-5) & D(-4,-2)

To Find :

Area of a quadrilateral

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Area of Quadrilateral =∆ABC+∆ADC

First we find area of ∆ABC

X1=-4,X2=0 ,X3=5

Y1=5,Y2=7 ,y3=-5

$\bold{\boxed{∆ABC = \frac{1}{2} [x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)]}}$

$∆ABC = \frac{1}{2} [- 4(7 - ( - 5) + 0( - 5 - 5) + 5(5 - 7)]$

$∆ABC = \frac{1}{2} [- 4(12) + 0 + 5( - 2)]$

$∆ABC = \frac{1}{2} ( - 48 - 10)$

$= \frac{1}{2} \times - 58 = - 29$

since,area can't be negative so ,

$\bold{\boxed{∆ABC=29sq.units}}$

Now.,finding area of ∆ADC

X1=-4,X2=-4 ,X3=5

Y1=5,Y2=-2 ,y3=-5

$∆ADC = \frac{1}{2} [ 4( - 2 - ( - 5) + ( - 4)( - 5 - 5) + 5(5 - ( - 2)]$

$= > \frac{1}{2} [- 4( - 2 + 5) - 4( - 10) + 5(5 + 2)]$

$= \frac{1}{2} [ - 4 \times 3 + 40 + 35]$

$= > \frac{1}{2} ( - 12 + 75)$

$= > \frac{1}{2} \times 63 = \frac{63}{2}$

$\bold{\boxed{∆ADC= \frac{1}{2} \times 63 = \frac{63}{2}}}$

Area of Quadrilateral=∆ABC+∆ADC

$\bold{= 29 + \frac{63}{2} = \frac{58 + 63}{2} = \frac{121}{2} sq.units}$

Answer 2

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Answer:

Given (−4,5),(0,7),(5,−5) and (−4,2)

To Find: Find the area of quadrilateral.

Let us Assume A(x

1

,y

1

)=(−4,5)

Let us Assume B(x

2

,y

2

)=(0,7)

Let us Assume C(x

3

,y

3

)=(5,−5)

Let us Assume D(x

4

,y

4

)=(4,−2)

Let us join Ac to form two triangles ΔABC and ΔACD

Area of triangle

=

2

1

[x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)]

Then, Area of given triangle ABC

=

2

1

∣−4(7+5)+0(−5−5)+5(5−7)∣

=

2

1

[−48+0−10]

=

2

58

Area of given triangle ABC

=

2

1

∣−4(−5+2)+5(−2−5)−4(5+5)∣

=

2

1

∣−4(−3)+5(−7)−4(10)]

=

2

1

∣12−35−40∣

=

2

1

∣−63∣

=

2

63

square units

Area of quadrilateral ABCD = Area of ABC + Area of ACD

=∣

2

58

+

2

63

∣

Hence, Area of Quadrilateral ABCD=

2

121

sq units.

Explanation:

GUY'S LET ME TELL U THIS LOOKS LIKE ITS LONG BUT NOW JUTS I WROTE IN THTA MANNER SO PLS MAKE SURE THAT READ THIS WHOLE ANSWER ❤️❤️