The area of ​​a quadrilateral whose vertices are

Hasan Azn

Hasan Azn

Answered question

2022-06-23

The area of ​​a quadrilateral whose vertices are O(0,0), M(4,1), I(5,3), L(3,4) is

Answer & Explanation

Vasquez

Vasquez

Expert2023-05-22Added 669 answers

To find the area of a quadrilateral with vertices O(0,0), M(4,1), I(5,3), and L(3,4), we can use the Shoelace Formula. The Shoelace Formula allows us to calculate the area of a polygon given the coordinates of its vertices.
The formula is as follows:
A=12|(x1y2+x2y3++xny1)(y1x2+y2x3++ynx1)|
where (x1,y1),(x2,y2),,(xn,yn) are the coordinates of the vertices in order.
In our case, the vertices of the quadrilateral are O(0,0), M(4,1), I(5,3), and L(3,4). Plugging these values into the Shoelace Formula, we have:
A=12|(0·1+4·3+5·4)(0·4+1·5+3·3)|
Simplifying the expression, we get:
A=12|(0+12+20)(0+5+9)|
A=12|3214|
A=12·18
A=9
Therefore, the area of the given quadrilateral is 9 square units.

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