Lemmara logoLemmaraWorked solution

WMA11/01 Jan 2023, Question 6: Triangles and Sectors in Radians

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 10 marks

The question, in short

Stage plan: sector OBC with angle 2.4 radians and area 40 m², plus congruent triangles OAB and ODC, with AOD straight and 12.5 m. Find radius, angle AOB, total area and perimeter.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Use the sector area formula with angle 2.4 and area 40 to find the radius in m to 2 decimal places.

  1. 1½r² × 2.4 = 40
  2. 2r² = 80/2.4 = 33.33…
  3. 3r = 5.77 m

Answerr = 5.77 m

Part (b) · 1 mark

Using the straight line AOD of length 12.5 m and the radius, find angle AOB in radians to 2 decimal places.

  1. 1Angles AOB, BOC and COD make a straight line (π) and AOB = COD
  2. 2AOB = (π − 2.4)/2 = 0.37 radians

Answer0.37 radians

Part (c) · 3 marks

Combine the sector area with the areas of the two congruent triangles to get the total stage area in m² to one decimal place.

  1. 1OA = OD = 12.5/2 = 6.25 m
  2. 2Area of triangle AOB = ½ × 5.77 × 6.25 × sin 0.37 = 6.54 m²
  3. 3Total area = 40 + 2 × 6.54 = 53.1 m²

Answer53.1 m²

Part (d) · 4 marks

Add the arc BC and the four straight edges AB, BC, CD, DA to find the total perimeter in m to one decimal place.

  1. 1Arc BC = 5.77 × 2.4 = 13.86 m
  2. 2AB² = 6.25² + 5.77² − 2 × 6.25 × 5.77 × cos 0.37, so AB = 2.27 m
  3. 3Perimeter = 12.5 + 2 × 2.27 + 13.86
  4. 4= 30.9 m

Answer30.9 m

Stuck on a step? Read the free lesson: Triangles and Sectors in Radians

Practise more triangles and sectors in radians questions

Real XMA01 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on triangles and sectors in radians

Also searched as: WMA11 January 2023 · WMA11/01 · wma11 jan23 · IAS Maths Pure Mathematics 1 January 2023 · question 6.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.