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To the nearest tenth, what is the area of the shaded segment when JA=8ft ??

A. 27.7 ft squared
B. 33.5 ft squared
C. 5.8 ft squared
D. 13.8 ft squared

To the nearest tenth what is the area of the shaded segment when JA8ft A 277 ft squared B 335 ft squared C 58 ft squared D 138 ft squared class=

Respuesta :

j4cek
[tex]A=\dfrac{1}{6}\pi 8^2-\dfrac{8^2\sqrt{3}}{4}\approx 5.8\;[ft^2][/tex]
Answer: C. 5.8 ft squared

Answer : The area of the shaded segment is 5.8 ft squared.

Explanation :

Given that,

Length of JA = 8 ft

We have to find the area of the shaded segment. It is given by :

Area of the shaded segment = area of sector - area of the triangle

[tex]A_{seg}=\dfrac{\theta}{360}\pi r^2-\dfrac{1}{2}r^2sin\theta[/tex]

[tex]A_{seg}=\dfrac{60}{360}\times \dfrac{22}{7}\times (8)^2-\dfrac{1}{2}\times (8)^2sin60[/tex]  

[tex]A_{seg}=5.8\ ft^2[/tex]

or

[tex]A_{seg}=5.8\ ft\ squared[/tex]

So, the correct option is (C) " 5.8 ft squared".

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