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Geometry in Everyday Life

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Geometry in Everyday Life

The fire station is planning a safer, more efficient training area. Use geometry to analyse its plan, solve practical problems and explain your design choices. Show working where needed.

Read the plan

The training area is a rectangle 18 m long and 12 m wide. A rectangular equipment bay, 6 m by 4 m, is attached along part of one 12 m side. A square practice pad has side length 5 m. Jai marks the corners of the main rectangle A, B, C and D in order, starting at the top left and moving clockwise. The main rectangle has a 90° angle at each corner.

1.Sketch the main 18 m by 12 m rectangle and label A, B, C and D in clockwise order, with A at the top left. Mark the right angles.
2.How many lines of symmetry does the main rectangular area have? State the direction of each line.
3.Zach walks from A to C along the diagonal. What is the length of this path? Give your answer to 1 decimal place.
4.Mason places a straight hose from A to C. What two smaller angles does the diagonal make with the rectangle’s sides at A? Give each to 1 decimal place.

Measure and plan

Use the measurements in the plan to compare shapes and make a practical recommendation.

5.What is the perimeter of the main rectangular area? Show the calculation.
6.A square practice pad has a perimeter of 20 m. What is its area?
7.The equipment bay is a 6 m by 4 m rectangle attached along the outside of the main rectangle. What is the area of the combined floor plan? Assume the two regions do not overlap.
8.Which statement is true about every rectangle? Choose one.
  • All four sides are equal.
  • Opposite sides are equal and all four angles are 90°.
  • It has exactly one line of symmetry.
  • Its diagonals always meet at right angles.
9.The station wants to put a safety strip around the square practice pad. If one metre of strip costs $8.50, how much will the strip cost?
10.A circular hose reel has a radius of 0.35 m. Find its circumference to 2 decimal places. Use π ≈ 3.14.
11.The main area has a right angle at A. The diagonal AC splits it into two angles. Explain why those two angles add to 90°.

3 printable pages

  • Geometry in Everyday Life, page 1 of 3: Read the plan

    Page 1

  • Geometry in Everyday Life, page 2 of 3: Measure and plan

    Page 2

  • Geometry in Everyday Life, page 3 of 3: 11. The main area has a right angle at A. The diagonal AC splits it into two angles.…

    Page 3

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