Find the area of the shaded region.


 Apr 26, 2020

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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