When you arrange the N points in sequence around the polygon (clockwise or counterclockwise), the area is half the magnitude of the sum of the determinants of the points taken pairwise. The N determinants will also include the one involving the last point and the first one.
For example, consider the vertices of a triangle: (1,1), (2,3), (3,-1). Its area can be computed as
(1/2)*|(1*3-1*2) +(2*-1-3*3) +(3*1-(-1)*1)|
= (1/2)*|1 -11 +4| = 3
Its 43. All triangles add to 180 so 47 + 90 = 137. then subtract 180 - 137 and get 43
Answer:

Step-by-step explanation:
we are given that A robot is expected to filter pollution out of at least 350 liters of air and water.
Also It filters air at the rate of 50 liters per minute, and it filters water at the rate of 20 liters per minute.
The inequality for number of minutes the robot should filter air (A) and water (W) to meet this expectations can be writte as follows:

Hence the required inequality has been formulated.
Answer: √51
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a^2 + b^2 = c^2
a^2 + 7^2 = 10^2
a^2 + 49 = 100
a^2 = 51
√(a^2) = √51
a = √51
Answer:
the length is 10
Step-by-step explanation:
√(1 - 9)2 + (12 - 18)2 =
√(-8)2 + (-6)2 = √64 + 36 =
√100= 10