Question

I need the proof of finding the "Area of a quadrilateral using coordinate geometry" fast I WILL MARK AS BRAINLIEST

Answer 1

Step-by-step explanation:

Using coordinate geometry we can find area of

quadrilateral by the sum of area of two triangles obtained by drawing a diagonal.

Ex: Area of quadrilateral ABCD with diagonal AC=area of ∆ABC+Area of ∆ACD.

Answer 2

ANSWER✔

$\sf\dashrightarrow WHAT \:IS\:ARE\:of\: QUADRILATERAL\:?$

$\red{\text{NOTE:- THERE IS NO ANY FORMULA FIXED REGARDING A QUADRILATERAL.}}$

$\purple{\text{WE CAN FIND THE AREA OF QUADRILATERAL BY FOLLOWING WAY,}}$

$\sf\dashrightarrow area \:of\: quadrilateral\: can\: be \:find\: using \: the \:diagonals,$

$\sf\dashrightarrow i.e.., \:a \:diagonal\: makes \: a \: quadrilateral\:in\:two\:triangles.$

$\sf\therefore area\:of\:the\: quadrilateral\:can\:be\:written\:as,$

$\large{\boxed{\bf{ \star\:\: AREA\:OF\:QUADRILATERAL= \:sum\:of\: the\: area \: of\:two \:triangle\:\: \star}}}$

$\sf\large\therefore \: area\:of\:triangle\:(coordinate\: geometry)= \dfrac{1}{2} \times \bigg( x_1(y_2-y_3)+x_2(y_3-y_1)+ x_3(y_1-y_2) \bigg)$

$\red{\text{USING AREA OF TRIANGLE WE CAN FIND THE AREA OF QUADRILATERAL}}$

$\sf\underline\bold{AREA\:OF\:QUADRILATERAL\:(coordinate\:geametry)= sum\:of \: the\: area \: of\: two\:triangle}$

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