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40 votes
40 votes
Acellus Find the area of the shaded region. 60° 5 cm A = [?] cm2 Enter a decimal rounded to the nearest tenth.

User Farid Chowdhury
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1 Answer

17 votes
17 votes

hello

to solve this question, we simply need to apply the formula of area of a segment

the formula is given as


A_{\text{segment}}=(1)/(2)*(\theta-\sin \theta)* r^2

let's write out the variables given in the question


\begin{gathered} \theta=60^0 \\ r=5\operatorname{cm} \end{gathered}

we can now input those values into the equation


\begin{gathered} A_{\text{segment}}=(1)/(2)*(\theta-\sin \theta)* r^2 \\ A_{\text{segment}}=(1)/(2)*(60-\sin 60)*5^2 \\ A_{\text{segment}}=(1)/(2)*(60-0.8660)*25 \\ A_{\text{segment}}=(1)/(2)*1478.35 \\ A_{\text{segement}}=739.175\operatorname{cm}^2 \end{gathered}

to get the value of the area of the shaded region,


\text{area of shaded region=area of circle - area of segment}

let's calculate the area of the circle


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User TriandicAnt
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