Real-World Geometry Applications

Name:

Date:

🏗️ Part 1: Geometry in Architecture and Engineering

1. Look at the Auckland Sky Tower image. Which geometric shapes can you identify? (Circle all that apply)

Cylinder

Cone

Rectangular prism

Sphere

2. A bridge design uses parallel beams with a diagonal support beam crossing them. If one angle formed is 65°, what is the corresponding angle on the opposite side?

25°

65°

115°

125°

3. In a circular window design, if the radius is 1.5 metres, what is the diameter?

Diameter = _______ metres

4. A building's blueprint uses a scale of 1:200. If a room measures 3 cm on the blueprint, what is the actual length?

6 metres

60 metres

600 metres

6000 metres

🎨 Part 2: Art and Cultural Geometry

5. Māori tukutuku panels often use geometric patterns. Which transformation creates a pattern that looks identical when rotated 90°?

Translation

Reflection

Rotational symmetry

Enlargement

6. Describe one example of symmetry you can see in your everyday environment (home, school, or community):

7. A tessellation pattern uses regular hexagons. How many degrees is each interior angle of a regular hexagon?

Interior angle = _______ degrees

📐 Part 3: Scale and Real-World Problem Solving

8. An architect creates a model house at a scale of 1:50. If the model's roof is 20 cm long, what is the actual roof length?

Actual length = _______ metres

9. Extension Challenge: If the scale factor from a model to the real building is 1:50, and the model has a floor area of 80 cm², what is the actual floor area in square metres?

10. Explain why understanding geometry is important for one of these careers: architect, engineer, or artist.

11. Design Challenge: In the space below, sketch a simple building design that includes at least three different geometric shapes. Label each shape.