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Measurement in Floor Plans

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Measurement in Floor Plans

A family is planning a small renovation. Use the scale, room dimensions and costs below to check their plans. Show units in your answers and include working for calculations. Scale drawings are not intended to be measured with a ruler.

Plan A: a rectangular living room

The living room is 5.4 m long and 3.6 m wide. Plan A uses a scale of 1:100. A 1:100 scale means 1 unit on the plan represents 100 of the same units in real life.

Room

Actual dimensions

Living room

5.4 m × 3.6 m

1.At a scale of 1:100, how many centimetres long should the living room be on Plan A?

2.A different plan must fit on an A4 page. Which scale gives a smaller drawing of the living room: 1:50 or 1:100? Explain briefly.

3.The real room is 3.6 m wide. Calculate its width in centimetres on a 1:100 plan.

4.Calculate the living room’s floor area in square metres. Include the correct unit.

5.Flooring costs $42.50 per square metre. What is the cost of flooring the whole living room, before any extra allowance for offcuts?

Plan B: an L-shaped study

The study can be split into two non-overlapping rectangles. Rectangle A is 4 m × 3 m. Rectangle B is 2 m × 2 m. The shared boundary between the rectangles is inside the room, not an outside wall.

6.Calculate the total floor area of the L-shaped study by adding the areas of Rectangle A and Rectangle B.

7.The living room is 5.4 m × 3.6 m. A 1.2 m-wide doorway is the only gap in its skirting boards. How many metres of skirting board are needed?

8.A builder says that a 1:50 drawing of a 5.4 m wall will be 10.8 cm long. Is the claim correct? Show a conversion to justify your answer.

9.Draw a rectangular bedroom measuring 4 m × 3 m at a scale of 1:100. Add a 0.9 m door and a 1.5 m window, and label the room’s real dimensions. At this scale, show the door and window using their correct plan lengths.

Draw and label the scaled bedroom plan here. Use the dimensions and scale in Question 9.

10.Using the actual bedroom dimensions from Question 9, calculate the floor area.