Analysis and Approaches for IBDP Maths Ebook 1 | Page 125

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Paper 2 Section A – Areas and perimeters of segments
Example
The following diagram shows a circle with centre O and radius 35 cm.
The points A , B and C are on the circumference of the circle, and
(a) Find the area of the sector OACB .
(b) Find the area of the triangle OAB.
(c) Hence, find the area of the shaded segment ABC .
AOB ˆ � 0.7 radians .
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Solution
(a)
(b)
(c)
The required area
1 (35)
2
� (0.7)
2
(A1) for substitution
2
� 428.75 cm
A1 N2
The required area
1
� (35)(35)sin 0.7
2
(A1) for substitution
� 394.5833334
2
� 395 cm
A1 N2
The required area
�428.75 � 394.5833334
(A1) for correct approach
� 34.16666657
2
� 34.2 cm
A1 N2
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