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Real-World Geometry Applications
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Real-World Geometry Applications
A local group is planning a small shelter and its surrounding space. Use geometry to check designs, calculate dimensions and explain your reasoning. Show working where useful. Give units with measurements.
Angles and structure
Check the shelter's frame and roof geometry.
1.Two parallel horizontal beams are crossed by a diagonal brace. One acute angle at the crossing is 68°. What is the size of the vertically opposite angle, and why?
2.A roof truss is an isosceles triangle. Its two equal base angles are each 52°. Calculate the angle at the top of the truss.
3.A circular window has a radius of 0.75 m. Find its diameter and circumference. Give your circumference to 2 decimal places. Use π ≈ 3.14.
Scale and measurement
Use scale factors carefully: lengths and areas do not scale in the same way.
4.On a plan with scale 1:100, the shelter is 8.4 cm long. What is its actual length in metres?
5.A scale model is built at 1:25. A support post is 7.2 cm tall on the model. How tall is the real post in metres?
- 0.18 m
- 1.8 m
- 18 m
- 180 m
6.The model floor has an area of 96 cm² and is built at a scale of 1:25. Calculate the real floor area in square metres. Remember to square the length scale factor.
Surfaces and design choices
Apply geometry to materials and patterns.
7.The shelter's rectangular floor is 8 m by 5 m. A square storage space measuring 2 m by 2 m will not be covered with flooring. How many square metres of flooring are needed?
8.A regular hexagonal tile is being considered for a path. What is the size of each interior angle? Show how you know.
9.A path design uses a repeating pattern of regular hexagons. Explain why regular hexagons can fit around a point without gaps. Include the angle calculation.
10.Choose one geometry idea used in this design task—scale, angle properties, area or symmetry. Describe one way it helps an architect or builder avoid a practical problem.
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