SPM 2020 Add Maths Paper 2, Question 6Circular Measure

Solved on video in English · Form 5, Circular Measure · 5:43 video

The question

(a)

Diagram 3 shows a cardboard in the shape of a regular pentagon. There are five congruent sectors in the pentagon, each centred at a vertex of the pentagon, and each sector touches its two adjacent sectors. It is given that the perimeter of the yellow coloured region is 18(pi) cm. [Use pi = 3.142] (a) Find the side length, in cm, of the pentagon to the nearest integer.

(b)

142] (b) A red circle with maximum circumference is drawn in the yellow coloured region. Calculate the area, in cm², of the remaining yellow coloured region.

SPM 2020 Add Maths Paper 2, Question 6: the question as drawn in Eduly's video5:43

Part (a)

Step 1

Interior angle of a regular pentagon = (5 - 2)*180/5 = 108 degrees = the sector angle at each vertex.

5 more steps, each with the reason for it, in the full solution

Final answer

Side length = 12 cm

Where students lose marks

Watch out: 6 cm is only the radius; the side is two radii, 12 cm. Convert 108° to radians first.

Part (b)

8 more steps, each with the reason for it, in the full solution

Final answer

22.45 cm²

Where students lose marks

Watch out: red circle radius = centre-to-vertex distance − sector radius (10.208 − 6), not 6. Find the pentagon area with five triangles.

Watch every step of this question solved on video (5:43), with the reason behind each step and a box that checks your own answer.

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