107_H23_Finding Areas.docx Page 1 of 4 11/19/2013 MET 107 Homework 23 – Finding Areas 1. Select the first worksheet in a new workbook and change its name to “Coordinate_Method.” Note that using a “_” instead of a “ “ in the name will prevent the Cell Formula Macro from asking you to hit the cancel button numerous times. It will also give you an actual number in the Value column. 2. Use the coordinate method to find the area of the polygon shown in the figure below. 3. Print your spreadsheet using the macro. 4. Document your cell formulas using the macro. Your worksheet might look like the one shown below. (0,0) (7,6) (3,6) (3,4) (0,4) (9,4) (11,4) (2,0) (2,1) (11,0) (8,1) (8,0) Use a single concatenated text string in a merged cell. ="Area = " & ROUND(0.5*ABS(C22-D22),2) & " sq. in." Some cells not shown.107_H23_Finding Areas.docx Page 2 of 4 11/19/2013 5. Select the second worksheet in the workbook and change its name to “Trapezoid_Method_1”. Find the area under the curve: y = x2 + 4 for values of x = 0 to 10 using the Trapezoid Method. You are to use 20 panels to calculate dx. Print your spreadsheet and document your cell formulas using the macro. Your worksheet should look similar (except for the number of coordinates in the data set) to the one shown below. Be sure to find the percent difference between the value you calculate and the “exact” solution which is 373 1/3. 0204060801001201401600 2 4 6 8 10 12X-ValuesY-Valuesy = x2 + 4 ExacteApproximatExactDifference% Use 20 Panels to find the area. By integration, the exact area = 373 1/3 Format this cell as %107_H23_Finding Areas.docx Page 3 of 4 11/19/2013 6. Select the third worksheet in the workbook and change its name to “Trapezoid_Method_2”. 1. Use a standard worksheet format. 2. Create the graph of two functions. The first function is Y = X3 and the second function is Y = 3X + 2. This are NOT the same functions shown in the example at the bottom of this page. Format your axes and chart similar to what is shown below. Use a delta x of .25 otherwise you cross hatching will not intersect the curve correctly. Add the “cross-hatching” between the two functions by adding a singular additional data series to the chart. This cross hatching must be done with an increment of .25. Your X axis scale should range from 0 to 2. The exact area between the functions is 6.00. 3. Find the area between the two curves (from x = 0 to 2) using the Trapezoid Method as discussed in class using four (4) panels (The example used 6 for the Number of Panels). Print out your spreadsheet using the Grid and Header macro as well as the Cell Formula macro. Doing this at this time will keep the output to a reasonable length, especially the cell formulas. 4. Next select an appropriate number of panels to obtain an area that is within 0.04% (+/- .01%) of the exact area. You may need to perform several iterations of this process to obtain this level of accuracy. Show all your iterations on your spreadsheet. The exact area is 6.0. The figure below shows an example graph of two functions: y = 9 – x2 and y = -(5/3)x + 5. Your spreadsheet should be structured in a similar manner (ie showing the vertical bars) except you are using different functions.107_H23_Finding Areas.docx Page 4 of 4 11/19/2013 5. Make a copy of your graph, move it to a new sheet (“Chart1”) then print your graph on a single sheet of paper, with a header that includes your name and course number. 6. Print your worksheet, using the Grid and Header macro. This print out will include all your trials. When printing, select Print Preview and use Page Setup to Fit to: 1 page wide by x pages tall where x will produce readable pages. Note: If you choose to include spaces in the tab names, the computer will prompt you to continually enter a file name for every cell formula that exists. DO NOT PUT SPACES IN TAB