All explanations must be typed The supporting math work must

All explanations must be typed. The supporting math work must be near and suitable for copying or scanning. The final document should be saved and submitted as a single pdf file. Give the assignment the heading GEN ED ASSESSMENT|MATH 2318. Do not include your name in the assignment or in the file name. Submit your assignment to your instructor via Blackboard by the deadline established by your instructor. Linear Algebra Assessment Problem Definitions: A point is an ordered pair of integers. A figure is a polygon with: Point vertices Every vertex connects exactly two sides of the figure Every side connects exactly two vertices No sides cross between vertices A boundary point is a point on a side of a figure. An interior point is a point inside the figure. Examples of figures: There are two figures to the right. The smaller has four boundary points and two interior points. The larger has five boundary points and three interior points. Objective: Let x be the number of boundary points and let y be the number of interior points. Find a linear function A of x and y that calculates the area of a given figure. Organize an approach to finding the formula. Use the approach to find the formula. Create three very different examples for which the sum of boundary and interior points is larger than seven and show that the formula works for them. Find a useful application of this area calculation formula to a \"real-world\" problem and explain how to apply it.

Solution

1) if the polygon is constructed on a grid of equal distanced points, its area can be calculated using pick\'s theorem.

2) The formula for calculating area according to picks theorem is

A= y+ (x/2) -1

where A is area

y is number of interior points

x is number of boundary points.

3) In the given example,

area of the bigger polygon can be found out using pick\'s theorem

y=3; x=5

substituting in pick\'s theorem,

A= 3+ (5/2) -1

A= 4.5 units