Measurement, STD1 2026 HSC 29

The floor plan of a house has been drawn using a scale of \(1:100\).

What is the width of the bedroom in metres? (1 mark)
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The western wall of the living room is to be painted.
The wall is 2.7 m high and the windows are 900 mm high.
One litre of paint covers 12 square metres.
How many litres of paint are required for two coats of paint? Give your answer to 2 decimal places. (3 marks)
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a. \(3.6\ \text{m}\)

b. \(2.34\ \text{L}\)

Show Worked Solution

a. \(\text{Using 1000 mm = 1 metre:}\)

\(\text{Width}=3600\ \text{mm}= \dfrac{3600}{1000}\ \text{m} = 3.6\ \text{m}\)

b. \(\text{Western wall length}=5600\ \text{mm}=5.6\ \text{m}\)

\(\text{Window on western wall: 1200 mm wide (1.2 m), 900 mm high (0.9 m)}\)

\(\text{Area to paint}\)	\(=\text{Wall area}-\text{Window area}\)
	\(=5.6\times 2.7-1.2\times 0.9\)
	\(=15.12-1.08\)
	\(=14.04\ \text{m}^2\)

\(\text{Two coats}=2\times 14.04=28.08\ \text{m}^2\)

\(\text{Paint required}=\dfrac{28.08}{12}=2.34\ \text{L}\)