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Flauer [41]
3 years ago
5

) An engineer deploys a set of sensors. Each sensor reports its location as a point in two-dimensional space. The points are (2,

7), (8, 2), (6, 11), (6, 5), and (11, 6). Use determinants to calculate the area of the polygon formed by the sensors.
Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
8 0

Answer:

<em>The polygon area is </em>51.5 U^{2}<em />

Step-by-step explanation:

Points:

(2,7), (8,2), (6,11), (6,5), (11,6)

1. The area of the polygon could be calculate with the eqation:

A=\frac{1}{2}\left[\begin{array}{ccc}x_{1} &y_{1}\\x_{2} &y_{2}\\x_{3} &y_{3}\\x_{4} &y_{4}\\x_{5} &y_{5}\end{array}\right]

2. Replace the coordinates in equation for A:

A=\frac{1}{2}\left[\begin{array}{ccc}2&7}\\8&2\\6&11\\6&5\\11&6\end{array}\right]

3. Solve the determinant, and calculate A:

A=\frac{1}{2}\left[\begin{array}{ccc}2&7}\\8&2\\6&11\\6&5\\11&6\end{array}\right]\\A=\frac{1}{2}[(6)(7)+(11)(11)+(8)(6)+(6)(2)]-[(2)(11)+(6)(6)+(11)(2)+(8)(5)]\\A=\frac{1}{2}[42+121+48+12]-[22+36+22+40]\\A=\frac{1}{2}[223]-[120]\\\\A=\frac{1}{2}[103]=51,5 U^{2}

<em>The polygon area is </em>51.5 U^{2}<em />

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