Theme Park Engineer

Phase 1: Mission Briefing

Welcome, Theme Park Engineer! Learn about your mission.

🎢 Your Mission

Congratulations! You have been hired as the Lead Engineer for a brand-new theme park. Your job is to design ride platforms, calculate building materials, fill pools and fountains, and plan landscaping. Every decision requires calculating area, surface area, and volume.

Your park covers 50,000 square feet of land. You will use geometry formulas to design every part of the park, from ride footprints to 3D structures. Build the most amazing park possible!

1

Theme Park Engineer Registration

Enter your information and name your theme park to begin!

Engineer Name (Your Name)

Period

Date

🎢 Name Your Theme Park

Describe your park's theme and attractions in 2-3 sentences

2

Geometry Vocabulary Review

Before we start building, review the key formulas you will use throughout this project.

📐 Formula Reference Sheet

Triangle Area: A = ½ × b × h

Parallelogram Area: A = b × h

Trapezoid Area: A = ½(b1 + b2) × h

Rectangle Area: A = l × w

Prism Surface Area: SA = 2B + Ph

Rectangular Prism Volume: V = l × w × h

Area of a triangle with b = 10 ft, h = 6 ft:

Area of a rectangle 12 ft by 8 ft:

Volume of a box 5 ft × 4 ft × 3 ft:

What UNIT do we use for area vs. volume?

Triangle: A = 1/2 × 10 × 6 = 30 sq ft. Rectangle: A = 12 × 8 = 96 sq ft. Volume: V = 5 × 4 × 3 = 60 cubic ft. Area uses square units (ft²), volume uses cubic units (ft³).

📚 Support: Area measures how much flat space a shape covers (like painting a wall). It uses square units like ft². Volume measures how much space a 3D object holds inside (like filling a box with water). It uses cubic units like ft³.

3

Park Layout Overview

Your park has 50,000 sq ft of land. Study how it will be divided into zones. Calculate the area allocated to each zone.

Zone	Shape	Dimensions
🎢 Thrill Rides	Rectangle	200 ft × 80 ft
🎠 Kids Zone	Rectangle	120 ft × 100 ft
🍔 Food Court	Rectangle	80 ft × 60 ft
🛶 Parking	Rectangle	250 ft × 100 ft

Add up all 4 zones. How much land is used? How much is left over for paths and landscaping?

🌟 Challenge: If you wanted to add a water park zone that uses exactly 20% of the remaining land, what would its area be? Design its rectangular dimensions.

Phase 2: Park Research

Calculate areas for ride platforms and polygon-shaped attractions.

Area Calculator

Shape

Base / Length

Height / Width

Base 2 (trap.)

Select a shape and enter dimensions...

4

Triangle Ride Platforms

Several ride platforms in your park are triangular. Calculate the area of each platform. Remember: A = ½ × b × h

Ride Platform	Base (ft)	Height (ft)
🎢 Dragon Drop	16	12
🎲 Cyclone Spin	20	14
🚀 Rocket Launch	24	10

Which platform is largest? If each sq ft costs $15 to pave, how much would it cost to pave the largest one?

For Dragon Drop: A = 1/2 × 16 × 12 = 1/2 × 192 = 96 sq ft. Don't forget the 1/2!

📚 Support: The formula for a triangle is A = 1/2 × base × height. Think of it this way: a triangle is exactly half of a rectangle with the same base and height. So find the rectangle area first (b × h), then divide by 2.

5

Parallelogram & Trapezoid Attractions

Some attractions have parallelogram and trapezoid-shaped footprints. Calculate each area.

Parallelograms: A = b × h

Bumper Cars arena: b = 30 ft, h = 18 ft

Haunted House floor: b = 45 ft, h = 22 ft

Trapezoids: A = ½(b1 + b2) × h

Stage area: b1 = 40 ft, b2 = 60 ft, h = 25 ft

Gift shop: b1 = 20 ft, b2 = 32 ft, h = 15 ft

A parallelogram and a rectangle both have a base of 30 ft and height of 18 ft. Do they have the same area? Explain why or why not.

6

Composite Shape — Park Entrance

The park entrance is a composite shape: a rectangle (40 ft × 20 ft) with a triangle on top (base 40 ft, height 15 ft). Find the total area.

Rectangle area:

Triangle area:

Total composite area:

Phase 3: Blueprint Planning

Calculate surface area for materials and volume for structures.

Surface Area & Volume Calculator

Length (ft)

Width (ft)

Height (ft)

Enter dimensions to calculate SA & Volume...

7

Surface Area — Painting Buildings

You need to paint the exterior walls and roof of park buildings (rectangular prisms). Calculate the surface area to determine how much paint to buy. SA = 2lw + 2lh + 2wh

Building	Length	Width	Height
🏪 Ticket Booth	8 ft	6 ft	10 ft
🍔 Snack Stand	12 ft	10 ft	9 ft
🎫 Gift Shop	20 ft	15 ft	12 ft

One gallon of paint covers 350 sq ft. How many gallons are needed for the Gift Shop? (Round up!)

For the Ticket Booth: SA = 2(8×6) + 2(8×10) + 2(6×10) = 2(48) + 2(80) + 2(60) = 96 + 160 + 120 = 376 sq ft. Think of it as finding the area of all 6 faces.

📚 Support: A rectangular prism has 6 faces. There are 3 pairs of matching faces: top/bottom (l×w), front/back (l×h), and left/right (w×h). Find each pair's area, multiply by 2, then add all three together.

8

Unfolding Nets — Material Planning

When you unfold a 3D shape flat, you get its net. This helps engineers plan how to cut materials. A rectangular prism net has 6 rectangles.

A souvenir box is 10 in × 5 in × 8 in. List the area of each face, then find the total surface area.

Top/Bottom (10×5) × 2 =

Front/Back (10×8) × 2 =

Left/Right (5×8) × 2 =

Total SA =

9

Triangular Prism Rooftop

The park's main building has a triangular prism roof. Find the surface area of the roof (2 triangular faces + 3 rectangular faces). Triangle: base = 20 ft, height = 8 ft, slant sides = 10.8 ft each. Prism length = 30 ft.

Area of ONE triangle face:

Area of BOTH triangle faces:

Area of the 3 rectangular faces (bottom: 20×30, two slant sides: 10.8×30 each):

Total surface area of the triangular prism:

10

Volume — Filling Pools & Fountains

Your water features need to be filled! Calculate the volume of each rectangular pool. V = l × w × h

Water Feature	Length	Width	Depth
💦 Wave Pool	60 ft	40 ft	5 ft
⛲ Lazy River	100 ft	8 ft	3 ft
⛺ Fountain	15 ft	15 ft	2 ft

1 cubic foot = 7.48 gallons of water. How many gallons does the Wave Pool hold?

🌟 Challenge: If you need to fill the wave pool and it takes 500 gallons per minute, how long (in hours and minutes) would it take to fill the entire pool?

Wave Pool: V = 60 × 40 × 5 = 12,000 ft³. Gallons = 12,000 × 7.48 = 89,760 gallons.

Phase 4: Construction Build

Build structures and calculate final material costs!

11

Design Your Own Ride Structure

Design a custom ride building. Choose your own dimensions and calculate both surface area and volume.

🎢 Name your ride:

Length (ft)

Width (ft)

Height (ft)

Show your surface area calculation:

Surface Area =

Show your volume calculation:

Volume =

12

Landscaping — Sod, Mulch, and Gravel

Your park needs landscaping! Calculate area for sod (grass) and volume for mulch/gravel beds.

🌱 SOD (Grass) — Area

Rectangular lawn: 80 ft × 50 ft

Triangular garden: b=30ft, h=20ft

Total sod needed:

🌲 MULCH — Volume

Flower bed: 25ft × 10ft × 0.5ft deep

Path border: 60ft × 3ft × 0.25ft

Total mulch needed:

If sod costs $0.85 per sq ft and mulch costs $3.50 per cubic ft, what is the total landscaping cost?

13

Total Material Cost Summary

Add up all your material costs for the park construction.

🔴 MATERIAL COSTS

Paint (buildings):

Water (pools):

Landscaping:

Paving ($15/sq ft):

Total: $0

Write a paragraph explaining your park's construction costs. Which area was most expensive? Were any costs surprising?

🌟 Challenge: If the park owner gives you a budget of $50,000 for materials, are you over or under budget? By how much? What would you cut or add?

14

Volume Comparison — Storage Buildings

Compare the storage capacity of different building designs. Which holds the most?

Storage Building	Dimensions	Volume
Design A (tall & narrow)	10 ft × 10 ft × 20 ft
Design B (wide & short)	20 ft × 20 ft × 5 ft
Design C (balanced)	15 ft × 12 ft × 11 ft

Which design holds the most? Which uses the least surface area (and therefore the least building material)? Calculate all 3 surface areas to compare.

Phase 5: Engineer Portfolio

Review your park designs and submit your project.

Theme Park Engineer Score

--

out of 100 points

📐

Area Ace

🎲

Shape Master

📦

Surface Pro

💦

Volume Expert

🌟

Park Engineer

15

Self-Assessment Rubric

Rate your own work on each skill. Click a score for each category.

Area of Polygons

1

I struggled with area formulas

2

I calculated some areas with help

3

I calculated areas correctly

4

I calculated all areas confidently

Surface Area

1

I couldn't find surface area

2

I found SA with some errors

3

I found SA accurately

4

I mastered surface area problems

Volume

1

I didn't understand volume

2

I calculated simple volumes

3

I calculated volumes accurately

4

I solved complex volume problems

Real-World Application

1

I didn't connect math to the park

2

I made some connections

3

I applied math well to designs

4

Every design was math-driven

16

Reflection Journal

Write thoughtful reflections about your learning.

1. What was the most challenging part of this project? How did you overcome it?

2. Give a real-world example (not from this project) where someone uses area, surface area, or volume.

3. Explain the difference between surface area and volume. When would an engineer use each one?

4. If you could redesign your park, what geometry concept would you use differently and why?

🎢

Park Construction Complete!

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🎢 Your Mission

📐 Formula Reference Sheet

Park Construction Complete!

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