The diagram shows a floor in the shape of a trapezium. John is going to paint the floor. Each 5 litre tin of paint costs £16.99 1 litre of paint covers an area of 2 m² John has £160 to spend on paint. Has John got enough money to buy all the paint he needs? You must show how you get your answer.

GCSE Edexcel Maths Rounding, Estimation & Bounds: The diagram shows a floor in the

The diagram shows a floor in the shape of a trapezium - Edexcel - GCSE Maths - Question 7 - 2018 - Paper 2

Question 7

The diagram shows a floor in the shape of a trapezium. John is going to paint the floor. Each 5 litre tin of paint costs £16.99 1 litre of paint covers an area of ... show full transcript

Worked Solution & Example Answer:The diagram shows a floor in the shape of a trapezium - Edexcel - GCSE Maths - Question 7 - 2018 - Paper 2

Step 1

Calculate the Area of the Trapezium

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Answer

To find the area of a trapezium, we use the formula:

ext{Area} = rac{1}{2} imes ( ext{Base}_1 + ext{Base}_2) imes ext{Height}

For this trapezium:

Base_1 = 10 m
Base_2 = 16 m
Height = 7 m

Substituting the values:

ext{Area} = rac{1}{2} imes (10 + 16) imes 7 = rac{1}{2} imes 26 imes 7 = 91 ext{ m}^2

Step 2

Calculate the Amount of Paint Needed

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Answer

Since 1 litre of paint covers 2 m², the total amount of paint needed is:

ext{Litres needed} = rac{ ext{Area}}{ ext{Coverage per litre}} = rac{91}{2} = 45.5 ext{ litres}

Step 3

Calculate the Number of Tins Required

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Answer

Each tin contains 5 litres, so the number of tins needed is:

ext{Tins needed} = rac{45.5}{5} = 9.1 ext{ tins}

Rounding up, John needs 10 tins.

Step 4

Calculate the Total Cost

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Answer

The cost for 10 tins of paint is:

ext{Total Cost} = 10 imes 16.99 = 169.90 ext{ pounds}

Step 5

Conclusion

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Answer

John has £160, but he needs £169.90 to buy all the paint. Therefore, John does not have enough money to buy the paint.

The diagram shows a floor in the shape of a trapezium - Edexcel - GCSE Maths - Question 7 - 2018 - Paper 2

Worked Solution & Example Answer:The diagram shows a floor in the shape of a trapezium - Edexcel - GCSE Maths - Question 7 - 2018 - Paper 2

Calculate the Area of the Trapezium

Calculate the Amount of Paint Needed

Calculate the Number of Tins Required

Calculate the Total Cost

Conclusion

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