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Parents Pricing Home GCSE Edexcel Maths Area & Perimeter The diagram shows a plan of Jason’s garden
The diagram shows a plan of Jason’s garden - Edexcel - GCSE Maths - Question 4 - 2022 - Paper 2 Question 4
View full question The diagram shows a plan of Jason’s garden.
ABCO and DEFO are rectangles.
CDO is a right-angled triangle.
AFO is a sector of a circle with centre O and angle AOF = 9... show full transcript
View marking scheme Worked Solution & Example Answer:The diagram shows a plan of Jason’s garden - Edexcel - GCSE Maths - Question 4 - 2022 - Paper 2
Calculate the area of rectangle ABCO Only available for registered users.
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The area of rectangle ABCO can be calculated using the formula:
e x t A r e a = e x t l e n g t h i m e s e x t w i d t h = 7 e x t m i m e s 11 e x t m = 77 e x t m 2 ext{Area} = ext{length} imes ext{width} = 7 ext{ m} imes 11 ext{ m} = 77 ext{ m}^2 e x t A re a = e x t l e n g t h im ese x t w i d t h = 7 e x t m im es 11 e x t m = 77 e x t m 2
Calculate the area of rectangle DEFO Only available for registered users.
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The area of rectangle DEFO is:
e x t A r e a = e x t l e n g t h i m e s e x t w i d t h = 4 e x t m i m e s 9 e x t m = 36 e x t m 2 ext{Area} = ext{length} imes ext{width} = 4 ext{ m} imes 9 ext{ m} = 36 ext{ m}^2 e x t A re a = e x t l e n g t h im ese x t w i d t h = 4 e x t m im es 9 e x t m = 36 e x t m 2
Calculate the area of triangle CDO Only available for registered users.
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The area of triangle CDO can be calculated using the formula:
ext{Area} = rac{1}{2} imes ext{base} imes ext{height} = rac{1}{2} imes 7 ext{ m} imes 9 ext{ m} = 31.5 ext{ m}^2
Calculate the area of sector AFO Only available for registered users.
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The area of sector AFO with radius 7 m and angle 90° is:
ext{Area} = rac{1}{4} imes ext{Area of circle} = rac{1}{4} imes ext{π} imes (7 ext{ m})^2 \
= rac{1}{4} imes ext{π} imes 49 ext{ m}^2 \ \
= 12.25 ext{π} ext{ m}^2 \ \
ext{(approximately 38.48 m}^2\text{ for } ext{π} ext{ around } 3.14)
Calculate the total area of the garden Only available for registered users.
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The total area of the garden is:
e x t T o t a l A r e a = e x t A r e a A B C O + e x t A r e a D E F O + e x t A r e a C D O + e x t A r e a A F O = 77 e x t m 2 + 36 e x t m 2 + 31.5 e x t m 2 + 38.48 e x t m 2 = 183.98 e x t m 2 ext{Total Area} = ext{Area}_{ABCO} + ext{Area}_{DEFO} + ext{Area}_{CDO} + ext{Area}_{AFO} \ \
= 77 ext{ m}^2 + 36 ext{ m}^2 + 31.5 ext{ m}^2 + 38.48 ext{ m}^2 \ \
= 183.98 ext{ m}^2 e x t T o t a l A re a = e x t A re a A BCO + e x t A re a D EFO + e x t A re a C D O + e x t A re a A FO = 77 e x t m 2 + 36 e x t m 2 + 31.5 e x t m 2 + 38.48 e x t m 2 = 183.98 e x t m 2
Determine the number of bags needed Only available for registered users.
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To determine the number of bags of grass seed needed:
ext{Bags Needed} = rac{ ext{Total Area}}{ ext{Coverage per bag}} = rac{183.98 ext{ m}^2}{14 ext{ m}^2} \ \
ext{Bags Needed} ext{ (rounded up)} = 14
Calculate the total cost Only available for registered users.
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The total cost for the grass seed is:
e x t T o t a l C o s t = e x t B a g s N e e d e d i m e s e x t C o s t p e r b a g = 14 i m e s £ 10.95 = £ 153.30 ext{Total Cost} = ext{Bags Needed} imes ext{Cost per bag} = 14 imes £10.95 = £153.30 e x t T o t a lC os t = e x t B a g s N ee d e d im ese x t C os tp er ba g = 14 im es £10.95 = £153.30 Join the GCSE students using SimpleStudy...97% of StudentsReport Improved Results
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