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Find the area of the shaded region.

 

 Apr 26, 2020
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Hi guest!

 

To find the area of the shaded region, we can first find the area of the pizza slice looking thing (sorry I forgot what it's called), and then subtract the triangle from it.

 

Since we know that the radius is 3, the area of the whole circle is 3^2*pi= 9pi. The pizza slice shape thing is 60 degrees, which is 1/6 of the whole circle (360/60=6). So the pizza slice shape thing is \(9\pi*\frac{1}{6}=\frac{3}{2}\pi\). This is equal to \(\approx 4.712\)

 

Now, let's find the area of the equilateral triangle (we know it's equilateral since the 2 sides are equal to 3, which means the other 2 angles are also 60 degrees). The formula for the area of an equilateral triangle is \(\frac{\sqrt{3}}{4}a^2\). So, the area of the triangle is \(\approx 3.897\)

 

Now, we just have to subtract \(4.712\) and \(3.987\).

\(4.712-3.987=0.725\) which is closest to \(\boxed{0.8\text{u}^2}\)

 

I'm not sure this is the correct answer, so please let me know if it's right!

:)

 Apr 26, 2020

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