Edexcel GCSE Maths (1MA1), Higher tier · Geometry and measures
Practise Area and perimeter. 1 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.
Question 1Easy2 marks
The diagram shows a triangle. Diagram NOT accurately drawn
[object Object]
Work out the area of the triangle.[2]
Show the answer and mark scheme
Answer: \(32\) cm²
M1 for \(\frac{1}{2} \times 16 \times 4\)
A1 for 32
Worked solution: Area \(= \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 16 \times 4 = 32\) cm²
Question 2Medium3 marks
The circumference of a circle is 75.4 cm. Work out the area of the circle. Give your answer correct to 1 decimal place.[3]
Show the answer and mark scheme
Answer: \(452.4\) cm²
M1 for \(r = \frac{75.4}{2\pi}\) (= 12.00...)
M1 for \(\pi \times r^2\) using their \(r\)
A1 for 452.4 (452.41...)
Worked solution: \(2\pi r = 75.4\) so \(r = 12.00\ldots\) cm. Area \(= \pi \times 12.00\ldots^2 = 452.41\ldots\) = 452.4 cm² (1 d.p.)
Question 3Hard4 marks
The diagram shows two circles with the same centre. The radius of the larger circle is 15 cm. The area of the shaded region between the circles is 518 cm². Diagram NOT accurately drawn
[object Object]
Work out the radius of the smaller circle. Give your answer correct to 3 significant figures.[4]
Show the answer and mark scheme
Answer: \(7.75\) cm
M1 for the area of the large circle, \(\pi \times 15^2\) (= 706.85...)
M1 for \(\pi r^2 = 706.85\ldots - 518\) (= 188.85...)
M1 for \(r = \sqrt{\frac{188.85\ldots}{\pi}}\)
A1 for 7.75 (7.753...)
Worked solution: Large circle \(= \pi \times 15^2 = 706.85\ldots\) cm². Small circle \(= 706.85\ldots - 518 = 188.85\ldots\) cm². \(r = \sqrt{\frac{188.85\ldots}{\pi}} = 7.753\ldots\) = 7.75 cm (3 s.f.)