Survey of Mathematics

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Survey of Mathematics

MGF2106 (Survey of Mathematics): Geometry Project
Purpose: Work individually or as a group to complete various tasks related to geometry, to

enhance your understanding and answer the questions.

Assignment: Complete the project, compiling the various parts into a single document which is submitted to the Dropbox in Falcon Online. The Discussion Board in Falcon Online may be used to find classmates for working as a group. If you work as a group, each student must submit the project solutions to the Dropbox in Falcon Online by the posted due date with each participants’ name on the submission.

Format for Dropbox Submission:

  1. The submission should be a single document formatted as .docx, .doc, .rtf, or .pdf.

  2. The submission should be typed. If there are parts of the assignment that need to be

    drawn by hand, they should be done neatly, scanned, and included in the final submission. Please check with your instructor if you have questions about the format of the document.

  3. Put your name on the document. If you worked in a group, also list the names of the other students in the group.

Part 1: Town Map

You will design and draw a town map that incorporates many key geometric concepts.
The project should fit on an 8 1⁄2 by 11 piece of paper. It can be drawn by hand or done on the computer or a combination of both. Feel free to use as much color as you like.

Your town map must include a title of your town and elements (labeled with numbers) that meet the following requirements. You can add any other elements to your map that you like. However, 1 – 20 must be included and clearly labeled on your map.

1a – 1b

Two streets parallel to each other

2

A diagonal street that is a transversal to the parallel streets

3a – 3b

Two coffee shops that are located within corresponding angles

4a – 4b

Two gas stations that are located within alternate interior angles

5a – 5b

Two grocery stores that are located within alternate exterior angles

6a – 6b

Two streets perpendicular to each other

7

A street that is a ray

8

A street that is a line segment

9

A roundabout in the midpoint of a line segment

10

A path or bridge that connect two complementary angles

11

A path or bridge that connect two supplementary angles

12a – 12b

Two parks at vertical angles to each other

13

A hospital in the shape of a parallelogram and place in the interior of a right angle

14

A school in the shape of a trapezoid that is placed in an obtuse angle

15

A post office in the shape of a rhombus located in an acute angle

16

A courthouse in the shape of a pentagon located at a right angle

17a – 17b – 17c

Three swimming pools in the shape of triangles: 1 scalene; 1 isosceles; 1 equilateral

18

A hexagonal building

19

An octagonal building

20

A cylindrical sandbox inside one of the parks

Part 2: Calculations of Volume and Surface Area

Compute how much sand, water, or paint is necessary for each of the elements below. Show all work.

  1. 1)  Fill two of the pools with water. Each pool will be filled to a depth of 5 feet. The other necessary dimensions are given below.

    • The isosceles triangle pool: height 20ft and base 35ft

    • The equilateral triangle pool: height 52ft and base 60ft

  2. 2)  The sandbox must be filled with sand. The sandbox has a depth of 2ft and a diameter of 14ft.

  3. 3)  The exterior walls of the regular pentagon shaped courthouse must be painted. Each wall of the courthouse is 80ft by 18ft.

Part 3: Impact Question

Provide an example, or examples, of how the concepts covered in this project could be applied in life or future career choices other than in city planning or map making.