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trapecia [35]
3 years ago
15

Help me with this math question please its find the area <3

Mathematics
1 answer:
kirill115 [55]3 years ago
6 0

Answer:

9.628 cm²

Step-by-step explanation:

Let A be the area of the sector OAB

Let a be the area of the sector OCD

The shaded area = A − a

\begin{aligned}A &=\frac{1}{12} (\pi \times 7^{2}) \\&=12.828 \ldots\end{aligned}

\begin{aligned}a & = \frac{1}{12}\left(\pi \times 3.5^{2}\right) \\&=3.2 \ldots\end{aligned}

The shaded area ≈ 12.828 - 3.2 ≈ 9.628 cm²

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\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{  (3rd quadrant)} \end{gathered}

Also,

\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}

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