Points, Lines, Planes, and AnglesMeasurements and geometry play a central role in mathematics and science. Measurement is a systematic way of assigning a number to a subset of a set of identifiable objects which could be measured in size, length, width etc. Measurements enable students to assign a number to an attribute of an object such as length, width etc. measurements are endless attributes; for example they can be subdivided into smaller numbers to smallest level of precision. Geometry and measurements empower students to appreciate interrelationships between figures and discover proofs through performing several activities. Measurements assist students to compare an attribute measurement using numbers. Measurements of an attribute held by one object are compared with measurements of an attribute held by another object and this indirect comparison enables students to solve real life problems (; Schuetz, 2008).I have been hired as a manager by a Community Recreation Center (CRC) to redesign its rectangular shaped parking lot to accommodate 15 additional parking spaces from the current 36. The rectangular shaped parking lot measures 50yards in length by 40 yards in width. The current design of the parking lot has 36 parking spaces which enables it to accommodate 36 vehicles at any time. Each parking lines is estimated to measure 4 inches in width. The length and width of the parking lot is limited as it cannot be increased beyond the current measurements. Measurements of the current 36 parking spaces have not been provided. Measurements of existing parking space have not been provided however they are all rectangular in shape. In the existing design there is a driving aisle between 12 parking spaces and the next lot of 24 parking spaces totaling 36 parking spaces. The 24 parking spaces are divided into 12 each facing each other. The current design of the parking lot is shown below;The existing design of the parking lot enables vehicles to park without causing any congestion and pull out with ease. The challenge of the new manager is to design a parking lot that offers additional parking space but still enables motorists to pull in and out of the parking lot without causing congestion. As the manager hired by the Community Recreation Centre (CRC) I am required to determine the maximum number of angle parking spaces with an angle of 60The park must be repainted as one of the first steps of redesigning the parking lot. I have to make a number of assumptions in order to redesign the parking lot to accommodate the maximum possible number of angled parking spaces. Each parking space will measure 18feet in length and 9 feet in width. The main challenge that the manager faces is to determine the area in square feet to be occupied by the parking lot as measurements cannot be altered. The only thing that the manager can do is to reduce the size of each parking space. The parking lot is measured in yards as the unit of measurement of 50 yards in length and 40 yards in width. To make reasonable comparisons I must convert the unit of measurements in yards into unit of measurements in feet since the parking spaces will be measured in feet. The length of the parking lot in feet is therefore 50 yard divided by 1yard multiplied by 3 feet =150 feet. The width of the parking lot in feet is 40yard divided by 1yard multiplied by 3 feet=120feet (Tsao & Pan, 2013). The parking will be as follows after redesign;The parking spaces will take the form of a parallelogram. The area of a parallelogram is obtained by multiplying the length by the width. The area of one parking space will therefore be 18 feet *9 feet=162square feet. The total area of the entire parking lot in square feet is 150feet * 120 feet =18,000 square feet. The total number of parking spaces that can be obtained from the parking lot without including the parking lines and driving aisles are 18,000square feet divided by 162 square feet multiplied by 1 parking space=111 parking spaces. However, it will be impossible to service the parking lot without adequate driving aisles.I need to create 3 driving aisles in the new design that is 2 one way driving aisle and 1 one-way driving aisle. The area in square feet of one-way driving aisle is obtained by multiplying the width of the one-way driving aisle by the length of the parking lot that is 12feet*150feet=1,800square feet whereas the total area occupied by a two way aisle is 24feet*150feet=3,600square feet. The total area for the one-way driving aisles is therefore 2*1800square feet=3,600square feet. The total area to be covered by the 3 driving aisles will be 3,600square feet+ 3,600square feet=7,200 square feet. One parking space will be shaped as per the diagram below;The surface area covered by each parking space represents a plane and will measure 162 square feet; that is 18 feet*9 feet. Point A to point B represents the width of the parallelogram. The next step is to calculate the total area that will be taken up by the parking lines. To determine that I must count the number of parking lines which will measure 9 feet and the ones that will measure 18 feet. Note that one parking line measuring the width of the parking space demarcates the boundary between two parking spaces. I therefore must count just one parking line for each parking space. There are 60 parking lines measuring the width of each parking space. As for length of each parking space I must count each line measuring 18 feet. After counting these parking lines they came to 31 parking lines whereas. The reason being that some parking spaces especially the ones facing each other share the parking lines determining their length. The width of one parking line is 4inches which converts to 1.33 feet. This is because 1 inch is equivalent to 0.333 feet. The total area of one parking line measuring 9 feet will be 9feet*1.333feet=11.997square feet. The area of the 60 parking lines with the same measurements will be 60 lines/1 feet*11.997square feet=719.82. The area of parking line measuring 18 feet will be 18feet*1.33 feet=23.94square feet. The total area will be 23.94square feet multiplied by the 31 parking lines measuring 18 feet that is 23.94square feet*31 lines* 1 line=742.14square feet. The total space occupied by the parking lines will be 742.14 square feet + 719.82 square feet=1,461.96 square feet (http://education.ti.com/en/us/products/calculators/graphing-calculators).The total space in square feet that will be occupied by the parking lines and the driving aisles will be 7,200square feet+1,461.96 square feet =8, 661.96 square feet. This therefore means that the available space in the parking lot available to create parking spaces is total area of the entire parking lot in square feet less area to be occupied by parking lines plus that to be occupied by drive in aisles. Hence, 18000 square feet less 8, 661.96 square feet = 9,338.04 square feet. Assuming each parking space will measure 162 square feet that is 9 feet by 18 feet in a parallelogram then the total parking spaces that can be obtained of the parking lot will be 9,338.04 square feet divided by 162 square feet= 57parking spaces. As the manager I will inform the CRC management that it can add the parking spaces from the current 36 to 57 by adding an additional 21 new parking spaces (; http://illuminations.nctm.org/ActivityDetail.aspx?ID=125).In summary it is important to note that each parking line separating the parking spaces will be slanting at an equal gradient to the previous thus creating parallel lines by adding doted lines you can create a perfect parallelogram. The outcome is a plane whose distinct points are the intersection on the width of each parallelogram (). A number of assumptions have been made which include the measurement of parking spaces in parking line A and in all other parking line areas. The other assumption is that I yard is equivalent to 3 feet. Formulas used in the assignment include formulas to calculate the area of a rectangle which is length multiplied by width. This was used to calculate the surface area of a parking line. That is 0.4feet* 9 feet=3.6 square feet for example. The area of a parallelogram was also relied on which was Length multiplied by width to determine the surface area of each plane which formed each parking space (; Tsao & Lin, 2011).http://education.ti.com/en/us/products/calculators/graphing-calculatorshttp://illuminations.nctm.org/ActivityDetail.aspx?ID=125Schuetz, G. (2008). Approximating geometry measurement.(4), 58-58,60. Retrieved from http://search.proquest.com/docview/213728246?accountid=45049Tsao, Y., & Pan, T. (2013).The computational estimation and instructional perspectives of elementary school teachers., 1-15. Retrieved from http://search.proquest.com/docview/1440862387?accountid=45049Tsao, Y., & Lin, Y. (2011). The study of number sense and teaching practice., 1-14. Retrieved from http://search.proquest.com/docview/887907244?accountid=45049