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​

Answer 1

$\textbf{Given:}$

$\text{Points are}\;(-1,-1),(5,-2),(6,1)\;\text{and}\;(2,3)$

$\textbf{To find:}$

$\text{Area of the quadrilateral formed by the points}$

$\textbf{Solution:}$

$\text{Let the points be}$

$A(-1,-1),B(5,-2),C(6,1),D(2,3)$

$\textbf{Area of ABC:}$

${\triangle}_1=\dfrac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$

${\triangle}_1=\dfrac{1}{2}[-1(-2-1)+5(1+1)+6(-1+2)]$

${\triangle}_1=\dfrac{1}{2}[-1(-3)+5(2)+6(1)]$

${\triangle}_1=\dfrac{1}{2}[3+10+6]$

${\triangle}_1=\dfrac{19}{2}$

$\textbf{Area of ACD:}$

${\triangle}_2=\dfrac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$

${\triangle}_2=\dfrac{1}{2}[-1(1-3)+6(3+1)+2(-1-1)]$

${\triangle}_2=\dfrac{1}{2}[-1(-2)+6(4)+2(-2)]$

${\triangle}_2=\dfrac{1}{2}[2+24-4]$

${\triangle}_2=11$

$\textbf{Area of quadrilateral ABCD}$

$=\textbf{Area of triangle ABC}+\textbf{Area of triangle ABC}$

$=\dfrac{19}{2}+11$

$=\dfrac{19+22}{2}$

$=\dfrac{41}{2}$

$=20.5\;\text{square units}$

Answer 2

Step-by-step explanation:

Hello dear ,

To find the area of quadrilateral which coordinates are given A(-1,-1) B(5,-2) C(6,1) D(2,3).

By joining these points we get a quadrilateral ABCD.

so, area of this quadrilateral is given by in two steps, i) by dividing the quadrilateral into two parts ABD and BCD.( ii)then calculating the area of each part and by adding we get total area of quadrilateral.

Lets get start,

[by using formula area of triangle if its coordinates is given =1/2{x1 (y2-y3) +x2(y3-y1) + x3(y1-y2)}.]

Area of ABD = 1/2{(-1)(-2 - 3) + 5(3-(-1)) + 2(-1-(-2))}

=1/2{ 5+20+2}

= 27/2 squar unit. ......i)

Area of BCD = 1/2{5(1-3)+ 6(3+2) + 2(-2-1)}

= 1/2{ -10 +30 -6}

= 1/2{14}

= 14/2

= 7 square units.......ii)

Therefore area of quadrilateral ABCD

= (area of tri ABD + area of tri BCD)

=( 27/2 + 7) square units

= (27+14)/2

= 41/2

= 20.5 square units. answer.

Hope this answer help you.

Thanking you .