geometry

Part 1: Town Map

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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.

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1a – 1b

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Two streets parallel to each other

2

A diagonal street that is a transversal to the parallel streets

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3a – 3b

Two coffee shops that are located within corresponding angles

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4a – 4b

Two gas stations that are located within alternate interior angles

5a – 5b

Two grocery stores that are located within alternate exterior angles

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6a – 6b

Two streets perpendicular to each other

7

A street that is a ray

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8

A street that is a line segment

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9

A roundabout in the midpoint of a line segment

 

10

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A path or bridge that connect two complementary angles

11

A path or bridge that connect two supplementary angles

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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

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

16

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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

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19

An octagonal building

20

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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. 

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