The diagram shows a sector $$\(A O B\)$$ which is part of a circle with centre $$\(O\)$$ and radius $$\(6 \mathrm{~cm}\)$$ and with angle $$\(A O B=0.8\)$$ radians. The point $$\(C\)$$ on $$\(O B\)$$ is such that $$\(A C\)$$ is perpendicular to $$\(O B\)$$. The arc $$\(C D\)$$ is part of a circle with centre $$\(O\)$$, where $$\(D\)$$ lies on $$\(O A\)$$. Find the area of the shaded region. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_m20_qp_12 Year：2020 Question No：7
Answer:
\[
O C=6 \cos 0.8=4.18(0)
\]
Area sector \(O C D=\frac{1}{2}(\text { their } 4.18)^{2} \times 0.8\)
\[
\triangle O C A=\frac{1}{2} \times 6 \times \text { their } 4.18 \times \sin 0.8
\]
Required area \(=\) their \(\triangle O C A-\) their sector \(O C D\)
\(2.01\)
O C=6 \cos 0.8=4.18(0)
\]
Area sector \(O C D=\frac{1}{2}(\text { their } 4.18)^{2} \times 0.8\)
\[
\triangle O C A=\frac{1}{2} \times 6 \times \text { their } 4.18 \times \sin 0.8
\]
Required area \(=\) their \(\triangle O C A-\) their sector \(O C D\)
\(2.01\)
Knowledge points:
1.4.2 use the formulae in solving problems concerning the arc length and sector area of a circle (Including calculation of lengths and angles in triangles and areas of triangles.)
Solution:
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