Find the area of quadrilateral by the vertices (-3,4) (-5-6) (4,-1) (1

1.	Find the area of quadrilateral by the vertices (-3,4) (-5-6) (4,-1) (1,2)
Answer» Answer: 43sq.units Step-by-step explanation: Given, A = (-3 , 4) B = (-5 , -6) C = (4 , -1) D = (1 , 2) To Find :- AREA of the Quadrilateral. Formula Used :- $Area=\dfrac{1}{2}\left\|\begin{vmatrix}x_1&y_1\\x_2&y_2\end{vmatrix}+\begin{vmatrix}x_2&y_2\\x_3&y_3\end{vmatrix}+..+\begin{vmatrix}x_n&y_n\\x_1&y_1\end{vmatrix}\right\|$ Solution :- $x_1=-3,y_1=4$ $x_2=-5 , y_2 = -6$ $x_3=4 , y_3 = -1$ $x_4=1,y_4=2$ $Area=\dfrac{1}{2}\left\|\begin{vmatrix}-3&4\\-5&-6\end{vmatrix}+\begin{vmatrix}-5&-6\\4&-1\end{vmatrix}+\begin{vmatrix}4&-1\\1&2\end{vmatrix}+\begin{vmatrix}1&2\\-3&4\end{vmatrix}\right\|$ $=\dfrac{1}{2}\left\|(18+20)+(5+24)(8+1)+(4+6)\right\|$ = 1/2 \| 38 + 29 + 9 + 10 \| = 1/2 \|86\| = 86/2 = 43sq.units.

Find the area of quadrilateral by the vertices (-3,4) (-5-6) (4,-1) (1,2)

Answer»

Answer:

43sq.units

Step-by-step explanation:

Given,

A = (-3 , 4)

B = (-5 , -6)

C = (4 , -1)

D = (1 , 2)

To Find :-

AREA of the Quadrilateral.

Formula Used :-

$Area=\dfrac{1}{2}\left|\begin{vmatrix}x_1&y_1\\x_2&y_2\end{vmatrix}+\begin{vmatrix}x_2&y_2\\x_3&y_3\end{vmatrix}+..+\begin{vmatrix}x_n&y_n\\x_1&y_1\end{vmatrix}\right|$

Solution :-

$x_1=-3,y_1=4$

$x_2=-5 , y_2 = -6$

$x_3=4 , y_3 = -1$

$x_4=1,y_4=2$

$Area=\dfrac{1}{2}\left|\begin{vmatrix}-3&4\\-5&-6\end{vmatrix}+\begin{vmatrix}-5&-6\\4&-1\end{vmatrix}+\begin{vmatrix}4&-1\\1&2\end{vmatrix}+\begin{vmatrix}1&2\\-3&4\end{vmatrix}\right|$