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Parents Pricing Home GCSE Edexcel Maths Coordinate Geometry The diagram shows a floor in the shape of a trapezium
The diagram shows a floor in the shape of a trapezium - Edexcel - GCSE Maths - Question 6 - 2018 - Paper 2 Question 6
View full question 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
View marking scheme Worked Solution & Example Answer:The diagram shows a floor in the shape of a trapezium - Edexcel - GCSE Maths - Question 6 - 2018 - Paper 2
Calculate the area of the trapezium Only available for registered users.
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The area of a trapezium can be calculated using the formula:
ext{Area} = rac{1}{2} imes ( ext{Base}_1 + ext{Base}_2) imes ext{Height}
In this case, Base_1 is 10 m, Base_2 is 16 m, and the height is 7 m. Therefore:
ext{Area} = rac{1}{2} imes (10 + 16) imes 7 = rac{1}{2} imes 26 imes 7 = 91 ext{ m}^2
Determine the total coverage of the paint Only available for registered users.
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Each litre of paint covers an area of 2 m². Therefore, 1 tin (5 litres) covers:
5 e x t l i t r e s i m e s 2 e x t m 2 / e x t l i t r e = 10 e x t m 2 5 ext{ litres} imes 2 ext{ m}^2/ ext{litre} = 10 ext{ m}^2 5 e x t l i t res im es 2 e x t m 2 / e x t l i t re = 10 e x t m 2
Calculate the total number of tins needed Only available for registered users.
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To find the number of tins of paint needed, divide the total area by the coverage of one tin:
ext{Number of tins} = rac{91 ext{ m}^2}{10 ext{ m}^2/ ext{tin}} = 9.1 ext{ tins}
Since John cannot buy a fraction of a tin, he needs to round up to 10 tins.
Calculate the total cost for the paint Only available for registered users.
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The cost of one tin is £16.99, so the total cost for 10 tins is:
e x t T o t a l c o s t = 10 e x t t i n s i m e s £ 16.99 = £ 169.90 ext{Total cost} = 10 ext{ tins} imes £16.99 = £169.90 e x t T o t a l cos t = 10 e x t t in s im es £16.99 = £169.90
Determine if John has enough money Only available for registered users.
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John has £160, which is not enough to cover the total cost of £169.90. Therefore, the answer is:
No, John does not have enough money to buy all the paint he needs.
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